The order of a null matrix is :

The integral value of k for which the system of linear equations $kx + y + 2z = 0$, $ky = x - 3z$ and $2x + y + kz = 0$ has a non-zero solution is

Match List-I with List-II

Let $A$ be any invertible square matrix. Then

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If A is an invertible symmetric matrix, then A⁻¹ is

The matrix X for which $\begin{bmatrix}5 & 4\\1 & 1\end{bmatrix}X=\begin{bmatrix}1 & -2\\1 & 3\end{bmatrix}$ is

Let A and B be 3×3 matrices such that $A \neq B$. If $A^3 = B^3$ and $A^2B = B^2A$, then the determinant of $A^2 + B^2$ is:

If $A = \begin{bmatrix} 3 & 0 & -1 \\ 2 & 3 & 0 \\ 0 & 4 & 1 \end{bmatrix}$, then which of the following is/are correct ?

A. $|A| = 1$

B. $A$ is singular matrix.

C. $|adj A| = 1$

D. $|adj.(adj A)| = 1$

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