CUET Mathematics 2025 15 May Shift 2 PYQs

If A and B are two invertible matrices, then which of the following statements are correct?

(A) $|A^{-1}| = |A|^{-1}$

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

(C) $(AB)^{-1} = A^{-1}B^{-1}$

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

Choose the correct answer from the options given below:

If A is a matrix of order $m × n$ and $B$ is a matrix such that $AB^T$ and $B^TA$ are both well-defined matrices, then order of matrix B is

The system of equations

$x - 3y - 8z = -10$

$2x + 5y + \lambda z = 13$

$3x + y - 4z = 0$

has infinite number of solutions if the value of $\lambda$ is equal to: