CUET · MATHS · PYQ PAPER 2023

Let \(A\) and \(B\) be two invertible square matrices of same order, then which of the following is not correct?

A \((A B)^{-1}=B^{-1} A^{-1}\)
B \((A B)^T=B^T A^T\) where \(T\) stands for transpose
C If \(A^T=-A\), then \(A\) is a skew-symmetric matrix
D Multiplication of \(A\) and \(B\) is always commutative

Verified Solution

Answer & Solution

Correct Answer

(D) Multiplication of \(A\) and \(B\) is always commutative

Step-by-step Solution

Detailed explanation

Matrix multiplication is generally not commutative. \(AB \neq BA\) Therefore, "Multiplication of \(A\) and \(B\) is always commutative" is not correct.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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