Match the LIST-I with LIST-II

LIST-I	LIST-II
A. All positive integral powers of a symmetric matrix are	I. Unit matrix.
B. Positive odd integral powers of a skew-symmetric matrix are	II. Null matrix.
C. All the matrices which are both symmetric and skew-symmetric, are	III. Skew - Symmetric matrix.
D. All the square matrices whose each diagonal element is one and each non-diagonal element is equal to zero, are	IV. Symmetric matrix.

Choose the correct answer from the options given below:

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

Let A be a square matrix of order 3 such that $|A|=3$, then the value of $\frac{|adj(adjA)|}{|A|}$ is

If A is a square matrix of order 3 with $|A| = 4$, then the value of $|2\,adj\,A|$ is:

If $A = \begin{bmatrix}2 & 3 & 1 \\ 2 & -1 & 0\end{bmatrix}$ and $B^T = \begin{bmatrix}4 & 4 \\ 6 & -2 \\ 2 & 0\end{bmatrix}$, then $4A + B$ is

If $A = \begin{bmatrix}-2 & 2 & 0\\3 & 1 & 4\end{bmatrix}$ and $B = \begin{bmatrix}2 & 0 & -2\\7 & 1 & 6\end{bmatrix}$ are two matrices such that $-3A + 5B + 2C = 0$ then matrix C is equal to:

Let A be any square matrix of order n, then which of the following are true?

(A) $| \text{adj } A| = |A|^{n-1}$

(B) $|A^{-1}| = \frac{1}{|A|}$

(C) $| \text{adj } A| = |A|^n$

(D) $(A^T)^{-1} = (A^{-1})^T$

Choose the correct answer from the options given below: