If A is square matrix of order 3 with $|A| = 3$, then $|4 \text{ adj} A|$ is equal to :

If $A=\begin{bmatrix}0 & 1\\0 & 0\end{bmatrix}$, then $A^{1999}$ is equal to

If $57 \equiv x (\bmod 5)$, then the least positive value of $x$ is:

The solution set of the given inequation $\frac{2x+3}{x-1}<4 (x\neq1)$ is:

If A is a non-singular square matrix of order n, then which of the following are TRUE ?

A. $|adj A|=|A|^{n-1}$

B. $|adj A|=|A|^{n-2}$

C. $|adj (adj A)|=|A|^{(n-2)^2}$

D. $|adj (adj A)|=|A|^{(n-1)^2}$

Choose the correct answer from the options given below:

If $A' = \begin{bmatrix} -2 & 3 \\ 1 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} -1 & 0 \\ 2 & 3 \end{bmatrix}$

then $(3A + 2B)'$ is :

If $\begin{bmatrix} 5x + 8 & 7 \\ y + 3 & 10x + 12 \end{bmatrix} = \begin{bmatrix} 2 & 3y + 1 \\ 5 & 0 \end{bmatrix}$, then the value of $5x + 3y$ is equal to :