If A and B are two square matrices of order 'n', where $AB \neq BA$, then

If $\begin{bmatrix}2x+1 & 5x \\ 0 & y^2+1\end{bmatrix} = \begin{bmatrix}x+3 & 10 \\ 0 & 26\end{bmatrix}$ then the possible values of x + y are:

If $A = \begin{bmatrix} 6 & 4 \\ 5 & 3 \end{bmatrix}$ and $B = adj(A)$, then $|B|$ is equal to:

Which of the following statements are correct?

A. If $P$ and $Q$ are square matrices of same order, then $(PQ^T-QP^T)$ is a skew symmetric matrix.

B. The number of all possible matrices of order $3\times2$ with each entry either –1 or 1, is 64.

C. If $P$ is an invertible matrix, then $P^T$ is also invertible.

D. If $P$ and $Q$ are square matrices of the same order, then $|PQ|=|P|+|Q|$.

Choose the correct answer from the options given below:

Which of the following statement is/are correct?

(A) A square matrix $A = [a_{ij}]$ is called a symmetric matrix if $a_{ij} = a_{ji}$ for all $i, j$

(B) $A = [a_{ij}]_{m \times m}$ is a diagonal matrix if $a_{ij} = 0$ when $i = j$

(C) A square matrix $A = [a_{ij}]$ is called a skew symmetric matrix, if $a_{ij} = -a_{ji}$ for all $i, j$

(D) The multiplication of diagonal matrices of same order is commutative

Choose the correct answer from the options given below:

If A and B are square matrices of the same order 3, such that det (A) = 3 and AB = 3I, where I is an identity matrix of order 3. Then the value of det (B) is:

If $A = \begin{bmatrix} 2 & -1 & -2 \\ 0 & 2 & -1 \\ 3 & -5 & 0 \end{bmatrix}$, then the value of det (adj (2A)) is: