If the sum of a matrix A and its transpose is $\begin{bmatrix} -6 & 4 \\ 4 & 10 \end{bmatrix}$, then A is:

If A is square matrix of order 3 x 3 such that $a_{ij} = j - i$, then which of the following statements are correct?

(A) A is a symmetric matrix.

(B) A is a skew symmetric matrix.

(C) $|A| = 0$.

(D) A is a diagonal matrix.

Choose the correct answer from the options given below:

Let $\begin{vmatrix} x & 2 \\ 18 & x \end{vmatrix} = \begin{vmatrix} -4 & -2 \\ -8 & -4 \end{vmatrix}$. Then

(A) $x = -4$

(B) $x = -6$

(C) $x = 4$

(D) $x = 6$

Choose the correct answer from the options given below:

If $A = \begin{bmatrix} 3 & 7 \\ 4 & -2 \end{bmatrix}$, $X = \begin{bmatrix} \alpha \\ -2 \end{bmatrix}$, $B = \begin{bmatrix} 7 \\ 32 \end{bmatrix}$ and $AX = B$, then the value of the $\alpha$ is

Identify the correct statements.

(A) If $A$ is a non-singular matrix, then $A^{-1} = \frac{|A|}{(\text{adj } A)}$

(B) If $A$ is an invertible matrix then $\frac{1}{|A^{-1}|} = |A|$

(C) If $A$ and $B$ are two invertible matrices of the same order then $AB$ is also invertible matrix and $(BA)^{-1} = A^{-1}B^{-1}$

(D) If $A$ is an invertible matrix, then $A^T$ is also invertible and $(A^T)^{-1} = \frac{1}{(A^{-1})^T}$

Choose the correct answer from the options given below :

Let $A$ be a non singular matrix of order $n \times n$, Then $|\text{adj }(3A)|$ is equal to:

Which of the following matrices are invertible?

(A) $\begin{bmatrix} 2 & 2 \\ 3 & 3 \end{bmatrix}$

(B) $\begin{bmatrix} 2 & 3 \\ 3 & 2 \end{bmatrix}$

(C) $\begin{bmatrix} 3 & 2 \\ 2 & 3 \end{bmatrix}$

(D) $\begin{bmatrix} 3 & 3 \\ 3 & 3 \end{bmatrix}$

Choose the correct answer from the options given below: