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:

Let A be a square matrix. Then,

(A) $A + A^T$ is a symmetric matrix

(B) $A - A^T$ is a skew-symmetric matrix

(C) $AA^T$ is a skew-symmetric matrix

(D) $A^T A$ is a symmetric matrix

Choose the correct answer from the options given below :

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

A point $P(3a, -2b)$ lies in region $4x + 7y \leq (-3)$ which of the following options is true ?

If the matrix $\begin{bmatrix} a & -2 & 5b \\ 2 & 0 & -15 \\ 15 & 3c & 0 \end{bmatrix}$ is skew-symmetric, then the value of $a^2 + b^2 + c^2$ is:

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

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

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