If a matrix has 8 elements then the possible order(s) it may have

(A) $8 \times 1$

(B) $5 \times 3$

(C) $6 \times 2$

(D) $2 \times 4$

Choose the correct answer from the options given below:

If $A = \begin{bmatrix} 0 & 2 & -3 \\ y & 0 & -1 \\ z & x & 0 \end{bmatrix}$ is skew symmetric matrix, then $x^3 + y^3 + z^3 - 3xyz$ is equal to :

If $A = \begin{bmatrix}1 & 2\\ 0 & 3\end{bmatrix}$ then $|A. adj A|$ is

If a matrix $A = \begin{bmatrix} 5 & -8 \\ -3 & 5 \end{bmatrix}$ then which of the following is / are TRUE?

(A) $|A| = 1$

(B) $A$ is a singular matrix.

(C) $-2A = \begin{bmatrix} 10 & -16 \\ -6 & 10 \end{bmatrix}$

(D) $AI = \begin{bmatrix} 5 & 0 \\ 0 & 5 \end{bmatrix}$ $I$ is an identity matrix of order 2.

Choose the correct answer from the options given below:

If the matrix $\begin{bmatrix} 0 & -1 & 3x \\ 1 & y & -5 \\ -6 & 5 & 0 \end{bmatrix}$ is skew symmetric, then the value of $x+y$ is

The number of all possible matrices of order $2 \times 2$ with each entry 0 or 1 having their determinants as positive value is :

If $A^2 = 8A + kI, A = \begin{bmatrix} 1 & 0 \\ -1 & 7 \end{bmatrix}, I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ then value of $k$ is: