If A is a skew symmetric matrix, then $A^2$ is a

If $A = \begin{bmatrix} 1 & 2 & -3 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 3 \\ 7 & -8 \\ 1 & 2 \end{bmatrix}$, then which of the following are true?

(A) AB is a $2 \times 3$ matrix

(B) $B^2$ is a $3 \times 3$ matrix

(C) BA is not possible

(D) $A^3$ is not possible

Choose the correct answer from the options given below:

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) $x \neq y \neq z$

Choose the correct answer from the options given below:

If the matrix $\begin{bmatrix} 5 & x^2 \\ 3x-2 & x-1 \end{bmatrix}$ is symmetric, then values of $x$ are :

If $A = \begin{bmatrix} x & 1 \\ y & -1 \end{bmatrix}, B = \begin{bmatrix} 1 & -1 \\ 2 & -1 \end{bmatrix}$ and $(A+B)^2 = A^2 + B^2$, then

The matrix which is both symmetric and skew-symmetric, is a:

The real value of $a$ for which the system of equations $x+ay=0, y+az=0, z+ax=0$ has infinitely many solutions, is :