The inverse of is

The inverse of matrix is

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.

  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

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 a_max, 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 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 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

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

The inverse of the matrix is

The ad joint of is

The reaction of ethanol with  does not give:

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 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