Let $A = (a_{ij})$ and $B = (b_{ij})$ are square matrices of same order.

(A) The number of possible matrices of order $2 \times 2$ with entries $-1, 0, 1$ is 81.

(B) $A + A'$ is skew symmetric matrix

(C) $A \cdot A^{-1} = 0$, $|A| \neq 0$

(D) A is skew symmetric matrix if $a_{ij} = -a_{ji}$ for all $i, j$

(E) $(AB)' = A'B'$

Choose the correct answer from the options given below :

For two matrices $A = \begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{bmatrix}$ and $B^T = \begin{bmatrix} -1 & 2 & 1 \\ 1 & 2 & 3 \end{bmatrix}$, A - B equals

If $A = \begin{bmatrix} 0 & 1 & -3 \\ -1 & 0 & 5 \\ 3 & -5 & 0 \end{bmatrix}$, then the value of $|A^{2025}|$ is

If the matrix $\begin{bmatrix} -1 & x-y & 4 \\ 2 & 0 & 5 \\ x+y & z & 6 \end{bmatrix}$ is symmetric, then $x + 3y + 2z$ is equal to

If $A$ and $B$ square matrices of order 3 such that $|A| = -1$, $|B| = 5$, then the value of $|2AB|$ is:

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

If A is a square matrix of order 4 and $|adj\,A| = 8$, then $|A| =$