If A and B are two square matrices of same order such that $AB = A$ and $BA = B$, then the value of $A^{2024} + B^{2024}$ is equal to

The value of the expression $\frac{x^2 + y^2}{x - y}$ is:

If $A = \begin{bmatrix}1 & 2 & 3\\4 & 5 & 6\end{bmatrix}$ and $B = \begin{bmatrix}1 & 2\\3 & 4\\5 & 6\end{bmatrix}$, then $A + B$ is equal to

For every square matrix $A$ of order $n\times n$, which of the following statements are correct ?

(A) $(adjA)A = A(adjA) = |A|I$, where $I$ is identity matrix of order n.

(B) $|kA|=k^n|A|$, k is any scalar.

(C) $|adjA|=|A|^n$

(D) $A^2=A$

Choose the correct answer from the options given below:

If $A = \begin{bmatrix} 7 & 3 \\ 5 & -7 \end{bmatrix}$ be such that $A^{-1} = kA$, then $k$ equals

If $A=\begin{bmatrix}3 & -2 & 3 \\ 2 & 1 & -1 \\ 4 & -3 & 2\end{bmatrix}$ and $A(adjA)=xI$, where $I$ is an identify matrix of order 3, then $x$ is equal to

If $A^T = \begin{bmatrix} -2 & 3 \\ 1 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} -1 & 0 \\ 1 & 2 \end{bmatrix}$, then the matrix $(A + 2B)^T$ is