CUET Mathematics 2026 25th May Shift 1 PYQs

If $A$ is a square matrix of order $n \times n$, then which of the following are correct?

(A) $|kA| = k^n|A|$, $k$ is a constant

(B) $|k\ adjA| = k^n|adjA|^{n-1}$, $k$ is a constant

(C) $|adj\ adjA| = |A|^{(n-1)^2}$

(D) $A(adjA) = |A|I$, $I$ is an identity matrix of order $n$

Choose the correct answer from the options given below:

Which of the following statements are correct?

(A) Inverse of a matrix, if it exists, is unique

(B) $(kA)' = -kA'$ (where k is any real number)

(C) For an invertible matrix $A$, $(A^{-1})^{-1} = A$

(D) For an invertible matrix $A$, $(A')^{-1} = (A^{-1})'$

Choose the correct answer from the options given below:

Let A be a square matrix of order 3 and $|A| = -3$, then $|adj(3A)|$ is equal to: