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The inverse of matrix $A equals open square brackets table row 0 1 0 row 1 0 0 row 0 0 1 end table close square brackets$ is

A
$A^{T}$
$[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]$
$[\begin{matrix} 1 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{matrix}]$

The correct answer is: A

$A equals open square brackets table row 0 1 0 row 1 0 0 row 0 0 1 end table close square brackets$ $rightwards double arrow$ $vertical line A vertical line equals negative 1 left parenthesis 1 plus 0 right parenthesis equals negative 1$
$a d j left parenthesis A right parenthesis equals open square brackets table row cell A subscript 11 end subscript end cell cell A subscript 21 end subscript end cell cell A subscript 31 end subscript end cell row cell A subscript 12 end subscript end cell cell A subscript 22 end subscript end cell cell A subscript 32 end subscript end cell row cell A subscript 13 end subscript end cell cell A subscript 23 end subscript end cell cell A subscript 33 end subscript end cell end table close square brackets$
$fraction numerator left parenthesis negative 1 right parenthesis to the power of 3 plus 2 end exponent M subscript 32 end subscript over denominator negative 2 end fraction comma text end text equals fraction numerator negative left parenthesis negative 2 right parenthesis over denominator negative 2 end fraction equals negative 1$ $A subscript 11 end subscript equals 0 comma A subscript 12 end subscript equals negative 1 comma A subscript 13 end subscript equals 0$
$A subscript 21 end subscript equals negative 1 comma A subscript 22 end subscript equals 0 comma A subscript 23 end subscript equals 0$
$A subscript 31 end subscript equals 0$ , $A subscript 32 end subscript equals 0 comma A subscript 33 end subscript equals negative 1$
$fraction numerator left parenthesis negative 1 right parenthesis to the power of 3 plus 2 end exponent M subscript 32 end subscript over denominator negative 2 end fraction comma text end text equals fraction numerator negative left parenthesis negative 2 right parenthesis over denominator negative 2 end fraction equals negative 1 blank A to the power of negative 1 end exponent equals fraction numerator a d j left parenthesis A right parenthesis over denominator vertical line A vertical line end fraction equals open square brackets table row 0 1 0 row 1 0 0 row 0 0 1 end table close square brackets equals A$ .

A real number multiplicative inverse is the number that, when multiplied by the original number, produces 1 (the identity). Because a× 1/a= 1 is the multiplicative inverse of a. When the inverse of a matrix is multiplied by a given matrix, it produces a multiplicative identity. For example, the inverse of a matrix A is A-1 and A.A-1=A-1.A=I, where I is the identity matrix.
A square matrix with one on the diagonal and zeros everywhere else is known as an identity matrix. Think of the identity matrix as the matrix's prime number.
An invertible matrix is one for which it is possible to calculate the inverse matrix and for which the determinant is not zero.

$A space a n d space B$ respectively are

chemistry-General

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Light is incident normally in face AB of a prism as shown in figure A liquid of refractive index m is placed on face AC of the prism The prism is made of glass of refractive index 3/2 The limits of m for which total internal reflection takes place on face AC is

physics-General

General

physics-

An observer can see through a pin-hole the top end of a thin rod of height h, placed as shown in the figure The beaker height is 3h and its radius h When the beaker is filled with a liquid up to height 2h, he can see the lower end of the rod Then the refractive index of the liquid is

physics-General

General

physics-

A rectangular glass slab ABCD of refractive index n₁ is immersed in water of refractive index $n subscript 2 end subscript open parentheses n subscript 1 end subscript greater than n subscript 2 end subscript close parentheses$ A ray of light is incident a the surface AB of the slab as shown The maximum value of the angle of incidence a_max_, such that the ray comes out only from the other surface CD, is given by

physics-General

General

physics-

A light ray traveling in glass medium is incident on glass-air interface at an angle of incidence q The reflected (R) and transmitted (T) intensitites, both as function of q , are plotted The correct sketch is

physics-General

General

physics-

A point source S is placed at the bottom of different layers as shown in the figure The refractive index of bottom most layer is m₀ The refractive index of any other upper layer is $mu subscript left parenthesis n right parenthesis end subscript equals mu subscript 0 end subscript minus fraction numerator mu subscript 0 end subscript over denominator 4 n minus 18 end fraction text where end text n equals 1 comma 2 comma horizontal ellipsis horizontal ellipsis A$ ray of light with angle i slightly more than 30° starts from the source S Total internal reflection takes place at the upper surface of a layer having n equal to

physics-General

General

physics-

An insect starts moving up in a liquid from point O of variable refractive index $mu equals mu subscript 0 end subscript left parenthesis 1 plus a y right parenthesis$ where y is depth of liquid from the surface If u is the speed of insect, its apparent speed to the observer E immediatly after insect start moving

physics-General

General

maths-

If $A equals open square brackets table row 1 cell negative 2 end cell row 5 3 end table close square brackets$ , then $A plus A to the power of T end exponent$ equals

maths-General

General

maths-

The inverse of the matrix $open square brackets table row 3 cell negative 2 end cell row 1 4 end table close square brackets$ is

maths-General

General

maths-

The ad joint of $open square brackets table row 1 1 1 row 1 2 cell negative 3 end cell row 2 cell negative 1 end cell 3 end table close square brackets$ is

maths-General

General

chemistry-

The reaction of ethanol with $H subscript 2 S O subscript 4$ does not give:

chemistry-General

General

chemistry-

An aqueous solution of ethyl alcohol:

chemistry-General

General

physics-

A reflecting surface is represented by the equation $Y equals fraction numerator 2 L over denominator pi end fraction s i n invisible function application open parentheses fraction numerator pi x over denominator L end fraction close parentheses comma 0 0 less or equal than x less or equal than L$ A ray travelling horizontally as shown in figure and becomes vertical after reflection The coordinates of the point (s) where this ray is incident is

physics-General

General

physics-

A particle is dropped to move along the axis of a concave mirror of focal length f from a height f/2 as shown in the figure The acceleration due to gravity is g Find the maximum speed of the image

physics-General

General

physics-

The co-ordinates of image of point object P formed after two successive reflection in situation as shown in figure considering first reflection at concave mirror and then at convex

physics-General

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The inverse of matrix is

A

The correct answer is: A

, .

Related Questions to study

respectively are

respectively are

Light is incident normally in face AB of a prism as shown in figure A liquid of refractive index m is placed on face AC of the prism The prism is made of glass of refractive index 3/2 The limits of m for which total internal reflection takes place on face AC is

Light is incident normally in face AB of a prism as shown in figure A liquid of refractive index m is placed on face AC of the prism The prism is made of glass of refractive index 3/2 The limits of m for which total internal reflection takes place on face AC is

An observer can see through a pin-hole the top end of a thin rod of height h, placed as shown in the figure The beaker height is 3h and its radius h When the beaker is filled with a liquid up to height 2h, he can see the lower end of the rod Then the refractive index of the liquid is

An observer can see through a pin-hole the top end of a thin rod of height h, placed as shown in the figure The beaker height is 3h and its radius h When the beaker is filled with a liquid up to height 2h, he can see the lower end of the rod Then the refractive index of the liquid is

A rectangular glass slab ABCD of refractive index n1 is immersed in water of refractive index A ray of light is incident a the surface AB of the slab as shown The maximum value of the angle of incidence amax, such that the ray comes out only from the other surface CD, is given by

A rectangular glass slab ABCD of refractive index n1 is immersed in water of refractive index A ray of light is incident a the surface AB of the slab as shown The maximum value of the angle of incidence amax, such that the ray comes out only from the other surface CD, is given by

A light ray traveling in glass medium is incident on glass-air interface at an angle of incidence q The reflected (R) and transmitted (T) intensitites, both as function of q , are plotted The correct sketch is

A light ray traveling in glass medium is incident on glass-air interface at an angle of incidence q The reflected (R) and transmitted (T) intensitites, both as function of q , are plotted The correct sketch is

An insect starts moving up in a liquid from point O of variable refractive index where y is depth of liquid from the surface If u is the speed of insect, its apparent speed to the observer E immediatly after insect start moving

An insect starts moving up in a liquid from point O of variable refractive index where y is depth of liquid from the surface If u is the speed of insect, its apparent speed to the observer E immediatly after insect start moving

If , then equals

If , then equals

The inverse of the matrix is

The inverse of the matrix is

The ad joint of is

The ad joint of is

The reaction of ethanol with does not give:

The reaction of ethanol with does not give:

An aqueous solution of ethyl alcohol:

An aqueous solution of ethyl alcohol:

A reflecting surface is represented by the equation A ray travelling horizontally as shown in figure and becomes vertical after reflection The coordinates of the point (s) where this ray is incident is

A reflecting surface is represented by the equation A ray travelling horizontally as shown in figure and becomes vertical after reflection The coordinates of the point (s) where this ray is incident is

A particle is dropped to move along the axis of a concave mirror of focal length f from a height f/2 as shown in the figure The acceleration due to gravity is g Find the maximum speed of the image

A particle is dropped to move along the axis of a concave mirror of focal length f from a height f/2 as shown in the figure The acceleration due to gravity is g Find the maximum speed of the image

The co-ordinates of image of point object P formed after two successive reflection in situation as shown in figure considering first reflection at concave mirror and then at convex

The co-ordinates of image of point object P formed after two successive reflection in situation as shown in figure considering first reflection at concave mirror and then at convex

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The inverse of matrix $A equals open square brackets table row 0 1 0 row 1 0 0 row 0 0 1 end table close square brackets$ is

A
$A^{T}$
$[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]$
$[\begin{matrix} 1 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{matrix}]$

$A space a n d space B$ respectively are

$A space a n d space B$ respectively are

If $A equals open square brackets table row 1 cell negative 2 end cell row 5 3 end table close square brackets$ , then $A plus A to the power of T end exponent$ equals

If $A equals open square brackets table row 1 cell negative 2 end cell row 5 3 end table close square brackets$ , then $A plus A to the power of T end exponent$ equals

The inverse of the matrix $open square brackets table row 3 cell negative 2 end cell row 1 4 end table close square brackets$ is

The inverse of the matrix $open square brackets table row 3 cell negative 2 end cell row 1 4 end table close square brackets$ is

The ad joint of $open square brackets table row 1 1 1 row 1 2 cell negative 3 end cell row 2 cell negative 1 end cell 3 end table close square brackets$ is

The ad joint of $open square brackets table row 1 1 1 row 1 2 cell negative 3 end cell row 2 cell negative 1 end cell 3 end table close square brackets$ is

The reaction of ethanol with $H subscript 2 S O subscript 4$ does not give:

The reaction of ethanol with $H subscript 2 S O subscript 4$ does not give: