$A$ is skew-symmetric and $B$ is any square matrix of the same order. What is $B'AB$ ?

SymmetricCorrect answerYour answerSkew-symmetricCorrect answerYour answerThe zero matrixCorrect answerYour answerA diagonal matrixCorrect answerYour answer

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Correct answer: B

By the reversal law, $(B'AB)' = B'A'(B')' = B'A'B$ .
With $A' = -A$ , this is $-B'AB$ , so $B'AB$ is skew-symmetric. For a symmetric $A$ the same steps give a symmetric $B'AB$ .

Concept: Symmetry of products
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The rule this testsSymmetric and skew-symmetric matrices

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AAA is skew-symmetric and BBB is any square matrix of the same order. What is B′ABB'ABB′AB?

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$A$ is skew-symmetric and $B$ is any square matrix of the same order. What is $B'AB$ ?