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:

The inverse of the matrix $A = \begin{bmatrix} \frac{1}{2} & 0 & 0 \\ 0 & \frac{1}{4} & 0 \\ 0 & 0 & \frac{1}{8} \end{bmatrix}$ is

The value of $\begin{vmatrix} 1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2 \end{vmatrix}$ is:

If $A = \begin{bmatrix} 1 & 0 \\ -1 & 7 \end{bmatrix}$, $I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$, then the value of k so that $A^2 = 8A + kI$ is

If $\begin{vmatrix} 2x & 2 \\ 4 & x \end{vmatrix} = 10$, then $x$ is:

If $A=\begin{bmatrix}1&1&1\\1&0&2\\3&1&1\end{bmatrix}$ and $B=\begin{bmatrix}-2&0&2\\5&-2&-1\\1&2&-1\end{bmatrix}$ such that AB=4I (where I is identity matrix) then solution of system of equations $x+y+z=6, x+2z=7, 3x+y+z=12$ is

The matrix $A = \begin{bmatrix}-3 & 0 & 0\\0 & -3 & 0\\0 & 0 & -3\end{bmatrix}$ is a

A. Symmetric matrix

B. Scalar matrix

C. Diagonal matrix

D. Skew-symmetric matrix

Choose the correct answer from the options given below: