Aspire Faculty ID #17368 · Topic: CUET MCA 2026 · Just now
CUET MCA 2026

Assertion: A(BA) and (AB)A are symmetric matrices.

Reason: AB is symmetric matrix, if matrix multiplication of A with B is commutation.

Options:

(a) Assertion is true, Reason is true, and Reason is the correct explanation of the Assertion.

(b) Assertion is true, Reason is true, but Reason is not the correct explanation of the Assertion.

(c) Assertion is true, but Reason is false.

(d) Assertion is false, but Reason is true.

Solution

A(BA) = (AB)A = ABA

If A and B are symmetric matrices, then

(ABA)T = ATBTAT

Since A and B are symmetric,

AT = A and BT = B

Therefore

(ABA)T = ABA

Hence A(BA) and (AB)A are symmetric matrices.

Also, AB is symmetric if AB = BA (i.e., A and B commute).

Correct Answer: (a) Assertion is true, Reason is true, and Reason is the correct explanation of the Assertion.

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