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

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The set of all values of $\alpha$ for which the system of linear equations

$x + y + z = 1$

$x + 2y + 4z = \alpha$

$x + 4y + 10z = \alpha^2$

is consistent, is

Let $A = \begin{bmatrix} 1 & 2 & 1 \\ -1 & 3 & 2 \\ 2&4&1\end{bmatrix}$ and $M_{ij}$, $A_{ij}$ respectively denote the minor, co-factor of an element $a_{ij}$ of matrix A, then which of the following are true?

(A) $M_{22} = -1$

(B) $A_{23} = 0$

(C) $A_{32} = 3$

(D) $M_{23} = 1$

(E) $M_{32} = -3$

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If $A=\begin{bmatrix}1 & 1 & 1\\1 & 0 & 3\\1 & -2 & 1\end{bmatrix}$, then

Match List-I with List-II

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Let A be a non-singular matrix of order 3 and $|A| = 15$, then $|adj A|$ is equal to

Let $A=\begin{bmatrix}1 & 0 \\ -1 & 7\end{bmatrix}$ and $B=\begin{bmatrix}0 & 4 \\ -1 & 7\end{bmatrix}$ then

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For some constant 'k', if the system of linear equations

$2x - y + 3z = 1$

$x - 2y + z = 3$

$kx + y - z = 0$

has a unique solution, then