Question

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

- AB, BA
- AB, A
^{2}
- A
^{2}, B^{2}
- AB, B
^{2}

^{2}^{2}, B^{2}^{2}## The correct answer is: AB, B^{2}

### 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.

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

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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 =

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 only.

Statement - II The maximum value of sin x + cos x occurs when x =

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.