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:

If A is a square matrix of order 3, B = kA and |B| = $x$|A| then,

If $A = \begin{bmatrix} 2 & -2 & 1 \\ 0 & 4 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & -2 & 7 \\ 2 & 0 & 6 \end{bmatrix}$ are two matrices such that $3A - 2B + 4C = 0$, then matrix $C$ is equal to:

Let $A$ and $B$ be two non-singular, square matrices of same order, and

A. $(AB)^{-1} = B^{-1} \cdot A^{-1}$

B. $(A+B)^{-1} = B^{-1} + A^{-1}$

C. $adj. A = |A| \cdot A^{-1}$

D. $det(A^{-1}) = [det A]^{-1}$

Choose the correct answer from the options given below

$\Delta=\left|\begin{array}{ccc}1 & \cos x & 1 \\ -\cos x & 1 & \cos x \\ -1 & -\cos x & 1\end{array}\right|$

(A) $\Delta=2\left(1-\cos ^{2} x\right)$

(B) $\Delta=2\left(2-\sin ^{2} x\right)$

(C) Minimum value of $\Delta$ is $2$

(D) Maximum value of $\Delta$ is $4$

Choose the correct answer from the options given below :

If $A = \begin{bmatrix} 9 & 7 & 5 \\ 6 & 4 & 2 \\ 1 & 3 & 8 \end{bmatrix}$, then (cofactor of $a_{13}$ - cofactor of $a_{32}$ )will be equal to :

If matrix $A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$, then $A^2+I$ is equal to: (Where I is an identity matrix of order 2)