If $A = \begin{bmatrix}\frac{1}{4} & 2\\0 & 2x-3\end{bmatrix}$, $B = \begin{bmatrix}4 & 8\\0 & -1\end{bmatrix}$ and AB = $I_2$ (Identity matrix of order 2), then the value of $x$ is

Consider the matrices $A = \begin{bmatrix} 9 & 0 & 0 \\ 0 & 16 & 0 \\ 0 & 0 & 25 \end{bmatrix}$ and $B = \begin{bmatrix} \frac{1}{5} & 0 & 0 \\ 0 & \frac{1}{4} & 0 \\ 0 & 0 & \frac{1}{3} \end{bmatrix}$. The value of $|(AB)^{-1}|$ is

If $A=\begin{bmatrix}1 & 2\\2 & 1\end{bmatrix}$ and $f(x)=x^2-2x-3$, then $f(A)$ is equal to

If $A$ is a skew-symmetric matrix and $n$ is an odd positive integer, then $A^n$ is :

If A and B are two non-singular matrices of same order, then which of the following statements are not correct ?

A. AB is non singular.

B. $(A+B)^{-1} = B^{-1}+A^{-1}$.

C. adj (AB) = adj B. adj A.

D. AB is not invertible.

Choose the correct answer from the options given below:

The values of $x$ and $y$ in the equation $2\begin{bmatrix} x & 1 \\ 4 & -3 \end{bmatrix} + 3\begin{bmatrix} -2 & 1 \\ 2 & y-2 \end{bmatrix} = \begin{bmatrix} 2 & 5 \\ 14 & 3 \end{bmatrix}$ are respectively:

Which of the given values of $x$ and $y$ make the following pair of matrices equal ?

$\begin{bmatrix}2x-1 & 4\\y-1 & 3+2x\end{bmatrix}$ and $\begin{bmatrix}0 & y-2\\5 & 4\end{bmatrix}$