If A is a square matrix of order 3 and $|A| = 5$, then $|adj(adjA)|$ is :

If $A = \begin{bmatrix} 1 & 2 \\ 4 & -3 \end{bmatrix}$ and $f(x) = 2x^2 - 4x + 5$, the $f(A)$ is equal to

If $A = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & 2 \\ 2 & 0 \end{bmatrix}$, then the matrix AB is equal to

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

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 :

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

If $A = \begin{bmatrix} 0 & 0 & \sqrt{7} \\ 0 & \sqrt{7} & 0 \\ \sqrt{7} & 0 & 0 \end{bmatrix}$, then $|\text{adj } A|$ is equal to