If $A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$ then $A^{-1}$ is equal to

If A and B are invertible matrices of the same order, then $(AB)^{-1}$ is equal to

If $A = \begin{bmatrix} 1 & a \\ b & 2 \end{bmatrix}$ and $B = \begin{bmatrix} a & 1 \\ 2 & -3b \end{bmatrix}$ such that $\lvert AB\rvert = \lvert 2B\rvert$ and $ab \neq -\dfrac{2}{3}$ then:

A. $\lvert A\rvert = 2$

B. $\lvert A\rvert = 4$

C. $\lvert B\rvert = 2$

D. $\lvert B\rvert = 4$

Choose the correct answer from the options given below:

The system of equations

$x + ky = 0$

$3x + 5y = 0$

has infinitely many solutions, then k is equal to

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

Match List-I with List-II

Choose the correct answer from the options given below:

If the system of equations $2x + 5y = 7, 6x + \lambda y = 28$ is inconsistent, then

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