Let $A = \begin{bmatrix} 152 & 105 & 3 \\ 149 & 25 & 35 \\ 2 & 1 & 0 \end{bmatrix}$. If $A_{ij}$ denotes the co-factor of an element $a_{ij}$ of the matrix A, then the value of $a_{11}A_{21} + a_{12}A_{22} + a_{13}A_{23}$ is equal to

Let $\begin{vmatrix} 3x & -7 \\ 1 & 4 \end{vmatrix} = \begin{vmatrix} 3 & 2 \\ 4 & x \end{vmatrix}$, then value of $x$ is :

If $\begin{vmatrix} 2x & 5 \\ 8 & x \end{vmatrix} = \begin{vmatrix} 3 & 0 \\ 4 & -8 \end{vmatrix}$, then value(s) of x is/are

The value of $\begin{vmatrix} 1 & bc & bc(b+c) \\ 1 & ca & ca(c+a) \\ 1 & ab & ab(a+b) \end{vmatrix}$ is

If $A = [a_{ij}]$ is skew symmetric matrix of order 'n', then

If $A$ is a square matrix and $I$ is an identity matrix such that $A^{2}=A$, then $A(I-2 A)^{3}+2 A^{3}$ is equal to :

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 :