The number of all possible matrices of order 3 with each entry either 0 or 1 is:

If $\begin{bmatrix} 1 & 0 & 0 \\ 0 & y+1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 2x & \\ -2 & \\ z-3 & \end{bmatrix} = \begin{bmatrix} 6 \\ 4 \\ 1 \end{bmatrix}$ then $x + y + z$ is

If $A = \begin{bmatrix} x & 3 \\ 2 & 4 \end{bmatrix}$, $B = \begin{bmatrix} 2 & 3 \\ y & 3 \end{bmatrix}$ and $C = \begin{bmatrix} z & 1 \\ 8 & 2 \end{bmatrix}$ are singular matrices then:

(A) $x > y$

(B) $y > z$

(C) $z > x$

(D) $x \neq y \neq z$

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Let A = $[a_{ij}]_{n \times n}$ be a matrix. Then

Match List-I with List-II

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Which of the following statements are true?

(A) A matrix which is both symmetric as well as skew-symmetric is a null matrix.

(B) All positive integral powers of a symmetric matrix are symmetric.

(C) If A is a square matrix, then $A+A^T$ is a symmetric matrix.

(D) All positive even integral powers of a skew-symmetric matrix are skew-symmetric.

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If $A = [a_{ij}]_{3×3}$ where $a_{ij} = \begin{cases} (-1)^{i+j} - 1, & i = j \\ (-1)^{i+j}, & i \neq j \end{cases}$ then the value of $A + A^T$ is: