CUET Mathematics 2026 21st May Shift 1 PYQs

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:

Let $I = \begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}$ and $A = \begin{bmatrix}1 & -2\\2 & 4\end{bmatrix}$ be two matrices such that $8A^{-1} = kI - A, k \in \mathbb{R}$, then the value of $k$ is:

If the matrix $\begin{bmatrix}3 & 2a & -5\\4 & 0 & b\\-5 & 3 & 10\end{bmatrix}$ is symmetric, then the value of $5a + 2b$ is