If A is an invertible symmetric matrix, then A⁻¹ is

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 :

The matrix $\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}$ is a

(A) Null matrix

(B) Unit matrix

(C) Symmetric matrix

(D) Skew-symmetric matrix

Choose the correct answer from the options given below:

Which of the following statements is NOT CORRECT.

If $\begin{bmatrix}-2 & 0\\ x & 4\end{bmatrix}+3\begin{bmatrix}y & 0\\ 2 & -1\end{bmatrix}=I$, where $I$ is $2\times2$ unit matrix, then the value of $x$ and $y$ are:

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

If $A=\begin{bmatrix}x+4 & 3\\2 & 1\end{bmatrix}, B=\begin{bmatrix}5 & 2x-1\\2 & x\end{bmatrix}$ and $\lvert adj(AB) \rvert=32$, then the value of x is: