If $\begin{vmatrix}6 & 7\\ 3 & 8\end{vmatrix} = \begin{vmatrix}3x & 6\\ -1 & x\end{vmatrix}$, then the sum of values of $x$ is equal

If a matrix has 12 elements, then the possible orders it can have, are

(A) 1 × 12

(B) 4 × 3

(C) 6 × 3

(D) 6 × 2

Choose the correct answer from the options given below:

If the matrix $\begin{bmatrix}0 & \alpha & 2\\2 & \beta & 1\\\gamma & -1 & 0\end{bmatrix}$ is skew-symmetric, then $(\beta-\alpha-\gamma)$ equals

The determinant of which of the following matrices is a perfect square ?

A. $\begin{bmatrix}5&29\\-1&6\end{bmatrix}$

B. $\begin{bmatrix}5&26\\1&6\end{bmatrix}$

C. $\begin{bmatrix}10&3\\17&10\end{bmatrix}$

D. $\begin{bmatrix}8&5\\-3&-8\end{bmatrix}$

Choose the correct answer from the options given below:

Let $I = \begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}$ and $A = \begin{bmatrix}1 & -2\\2 & 4\end{bmatrix}$ be two matrices such that $8A^{-1} = kI - A, k \in \mathbb{R}$, then the value of $k$ is:

If $A = \begin{bmatrix} 2 & 1 & -1 \\ 0 & 1 & 2 \\ 2 & -1 & \lambda \end{bmatrix}$ is a singular matrix, then the value of $\lambda$ is

If A is a square matrix of order 3, B = kA and |B| = $x$|A| then,