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 $A = \begin{bmatrix} 7 & 3 \\ 5 & -7 \end{bmatrix}$ be such that $A^{-1} = kA$, then $k$ equals

If $A = \begin{bmatrix}1 & 2 & 3\\4 & 5 & 6\end{bmatrix}$ and $B = \begin{bmatrix}1 & 2\\3 & 4\\5 & 6\end{bmatrix}$, then $A + B$ is equal to

If $A = \begin{bmatrix} x & -3 & 4 \\ 3 & y & -5\\-4&z&0 \end{bmatrix}$ is a Skew-Symmetric matrix and $adj \ A = [a_{ij}]_{3 \times3}$, then $a_{11} + a_{22} + a_{33}$ is equal to

If matrix A is of order $2 \times 3$ and B of order $3 \times 2$, then

If $\begin{vmatrix}x&2\\18&x\end{vmatrix} = \begin{vmatrix}6&2\\18&6\end{vmatrix}$, then x equals:

If A is a square matrix of order 3 and $|A| = 4$, then the value of $|2A^T|$ is