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If A and B are matrices of order m × n and n × n respectively, then which of the following are defined-

AB, BA
AB, A²
A², B²
AB, B²

The correct answer is: AB, B²

To find the correct option.
Given, A and B are matrices of order m × n and n × n respectively.
For matrix multiplication, number of columns in first matrix must be equal to number of rows in second matrix.
Therefore, AB exists.
Also, $B squared$ exists since n = n.

Therefore, AB and $B squared$ are defined for the given matrices A and B.

The multiplicative inverse of A = $open square brackets table row cell cos invisible function application theta end cell cell negative sin invisible function application theta end cell row cell sin invisible function application theta end cell cell cos invisible function application theta end cell end table close square brackets$ is

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General

chemistry-

(A) and (B) are:

chemistry-General

General

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A = $open square brackets table row 1 2 2 row 2 1 2 row 2 2 1 end table close square brackets$ , then A³ – 4A² – 6A is equal to -

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General

maths-

Inverse of the matrix $open square brackets table row 3 cell – 2 end cell cell – 1 end cell row cell – 4 end cell 1 cell – 1 end cell row 2 0 1 end table close square brackets$ is

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General

maths-

If A = $open square brackets table row 2 cell – 1 end cell row cell – 1 end cell 2 end table close square brackets$ and A² – 4A – n I = 0, then n is equal to

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General

maths-

The value of x for which the matrix product $open square brackets table attributes columnalign center center center columnspacing 1em end attributes row 2 0 7 row 0 1 0 row 1 cell negative 2 end cell 1 end table close square brackets$ $open square brackets table row cell – x end cell cell 14 x end cell cell 7 x end cell row 0 1 0 row x cell – 4 x end cell cell – 2 x end cell end table close square brackets$ equal an identity matrix is :

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General

maths-

If A = $open square brackets table row 1 2 row 3 5 end table close square brackets$ , then A^–1 is equal to :

maths-General

General

maths-

If A is a singular matrix, then adj A is :

maths-General

General

Maths-

Statement - I The value of x for which (sin x + cos x)^{1 + sin 2x} = 2, when 0 ≤ x ≤ , is $straight pi divided by 4$ only.
Statement - II The maximum value of sin x + cos x occurs when x = $straight pi divided by 4$

In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason.

Statement - I The value of x for which (sin x + cos x)^{1 + sin 2x} = 2, when 0 ≤ x ≤ , is $straight pi divided by 4$ only.
Statement - II The maximum value of sin x + cos x occurs when x = $straight pi divided by 4$

Maths-General

In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason.

General

maths-

If [1 2 3 ]A = [4 5], the order of matrix A is :

maths-General

General

maths-

Let A and B be 3 × 3 matrices, then AB = O implies:

maths-General

General

maths-

If A = $open square brackets table row 1 2 row 3 cell negative 5 end cell end table close square brackets$ , B = $open square brackets table row 1 0 row 0 2 end table close square brackets$ and X is a matrix such that A = B X. Then X equals

maths-General

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If A and B are matrices of order m × n and n × n respectively, then which of the following are defined-

AB, BA AB, A2 A2, B2 AB, B2

The correct answer is: AB, B2

To find the correct option.Given, A and B are matrices of order m × n and n × n respectively.For matrix multiplication, number of columns in first matrix must be equal to number of rows in second matrix.Therefore, AB exists.Also, exists since n = n.

Related Questions to study

the products (A) and (B) are:

the products (A) and (B) are:

A matrix A = (aij) m x n is said to be a square matrix if-

A matrix A = (aij) m x n is said to be a square matrix if-

For any square matrix A = [aij], aij = 0, when i j, then A is-

For any square matrix A = [aij], aij = 0, when i j, then A is-

The multiplicative inverse of A =is

The multiplicative inverse of A =is

(A) and (B) are:

(A) and (B) are:

A = , then A3 – 4A2 – 6A is equal to -

A = , then A3 – 4A2 – 6A is equal to -

Inverse of the matrix is

Inverse of the matrix is

If A = and A2 – 4A – n I = 0, then n is equal to

If A = and A2 – 4A – n I = 0, then n is equal to

The value of x for which the matrix product equal an identity matrix is :

The value of x for which the matrix product equal an identity matrix is :

If A = , then A–1 is equal to :

If A = , then A–1 is equal to :

If A is a singular matrix, then adj A is :

If A is a singular matrix, then adj A is :

Statement - I The value of x for which (sin x + cos x)1 + sin 2x = 2, when 0 ≤ x ≤ , is only.Statement - II The maximum value of sin x + cos x occurs when x =

Statement - I The value of x for which (sin x + cos x)1 + sin 2x = 2, when 0 ≤ x ≤ , is only.Statement - II The maximum value of sin x + cos x occurs when x =

If [1 2 3 ]A = [4 5], the order of matrix A is :

If [1 2 3 ]A = [4 5], the order of matrix A is :

Let A and B be 3 × 3 matrices, then AB = O implies:

Let A and B be 3 × 3 matrices, then AB = O implies:

If A = , B = and X is a matrix such that A = B X. Then X equals

If A = , B = and X is a matrix such that A = B X. Then X equals

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AB, BA
AB, A²
A², B²
AB, B²

The correct answer is: AB, B²

To find the correct option.
Given, A and B are matrices of order m × n and n × n respectively.
For matrix multiplication, number of columns in first matrix must be equal to number of rows in second matrix.
Therefore, AB exists.
Also, $B squared$ exists since n = n.

For any square matrix A = [aij], aij = 0, when i $not equal to$ j, then A is-

For any square matrix A = [aij], aij = 0, when i $not equal to$ j, then A is-

A = $open square brackets table row 1 2 2 row 2 1 2 row 2 2 1 end table close square brackets$ , then A³ – 4A² – 6A is equal to -

A = $open square brackets table row 1 2 2 row 2 1 2 row 2 2 1 end table close square brackets$ , then A³ – 4A² – 6A is equal to -

Inverse of the matrix $open square brackets table row 3 cell – 2 end cell cell – 1 end cell row cell – 4 end cell 1 cell – 1 end cell row 2 0 1 end table close square brackets$ is

Inverse of the matrix $open square brackets table row 3 cell – 2 end cell cell – 1 end cell row cell – 4 end cell 1 cell – 1 end cell row 2 0 1 end table close square brackets$ is

If A = $open square brackets table row 2 cell – 1 end cell row cell – 1 end cell 2 end table close square brackets$ and A² – 4A – n I = 0, then n is equal to

If A = $open square brackets table row 2 cell – 1 end cell row cell – 1 end cell 2 end table close square brackets$ and A² – 4A – n I = 0, then n is equal to

If A = $open square brackets table row 1 2 row 3 5 end table close square brackets$ , then A^–1 is equal to :

If A = $open square brackets table row 1 2 row 3 5 end table close square brackets$ , then A^–1 is equal to :

Statement - I The value of x for which (sin x + cos x)^{1 + sin 2x} = 2, when 0 ≤ x ≤ , is $straight pi divided by 4$ only.
Statement - II The maximum value of sin x + cos x occurs when x = $straight pi divided by 4$

Statement - I The value of x for which (sin x + cos x)^{1 + sin 2x} = 2, when 0 ≤ x ≤ , is $straight pi divided by 4$ only.
Statement - II The maximum value of sin x + cos x occurs when x = $straight pi divided by 4$

If A = $open square brackets table row 1 2 row 3 cell negative 5 end cell end table close square brackets$ , B = $open square brackets table row 1 0 row 0 2 end table close square brackets$ and X is a matrix such that A = B X. Then X equals

If A = $open square brackets table row 1 2 row 3 cell negative 5 end cell end table close square brackets$ , B = $open square brackets table row 1 0 row 0 2 end table close square brackets$ and X is a matrix such that A = B X. Then X equals