Let A be any square matrix of order n, then which of the following are true? (A) $| \text{adj } A| = |A|^{n-1}$ (B) $|A^{-1}| = \frac{1}{|A|}$ (C) $| \text{adj } A| = |A|^n$ (D) $(A^T)^{-1} = (A^{-1})^T$ Choose the correct answer from the options given below:

If $A = \begin{bmatrix} -2 & 6 \\ -5 & -1 \end{bmatrix}$ then $A^{-1}$ is :

If $A = [a_{ij}]_{3\times3}$ is a square matrix, where $a_{ij} = i - j + 3$, then the value of $a_{21} + a_{31} - a_{23}$ is

If $x \neq y \neq z$ then $\begin{vmatrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \end{vmatrix}$ is equal to

For every square matrix $A$ of order $n\times n$, which of the following statements are correct ?

(A) $(adjA)A = A(adjA) = |A|I$, where $I$ is identity matrix of order n.

(B) $|kA|=k^n|A|$, k is any scalar.

(C) $|adjA|=|A|^n$

(D) $A^2=A$

Choose the correct answer from the options given below:

If $a$, $b$ and $c$ are distinct prime numbers then the value of $\begin{vmatrix} a-b & b-c & c-a \\ b-c & c-a & a-b \\ c-a & a-b & b-c \end{vmatrix}$ is equal to

If A is a square matrix such that $A^2 = A$ and I is the identity matrix of same order as A, then the value of $(A-2I)^2 - (2A + I)^2 + 11A$ is: