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Class 12 Matrices · Mcq Single Correct1 Markssymmetric_and_skew_symmetric

Class 12 Maths · Matrices · Mcq Single Correct #24

For arbitrary same-order real skew-symmetric matrices A and B, which condition is necessary and sufficient for AB to be symmetric?

(A) AB=O
(B) AB=−BA
(C) AB=BA
(D) BA=O

✅ Step-by-Step Solution

Final Answer: Option (C): AB=BA

(AB)ᵀ=BᵀAᵀ=(−B)(−A)=BA. Thus AB is symmetric if and only if AB=BA. Zero-product options are sufficient special cases, not a necessary condition.

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