Assertion (A): A matrix that is both symmetric and skew-symmetric is a zero matrix.
Reason (R): If $A' = A$ and $A' = -A$ , then $A = -A$ .

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Both conditions give the same $A'$ , so $A = -A$ , that is $2A = O$ .
So $A = O$ : R is true and explains A.

Concept: Symmetric and skew-symmetric combinations
Typical timeTypical: 90 s
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The rule this testsSymmetric and skew-symmetric matrices

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Ten questions from Matrices, at your own pace.

Assertion (A): A matrix that is both symmetric and skew-symmetric is a zero matrix.Reason (R): If A′=AA' = AA′=A and A′=−AA' = -AA′=−A, then A=−AA = -AA=−A.

Explanation

Assertion (A): A matrix that is both symmetric and skew-symmetric is a zero matrix.
Reason (R): If $A' = A$ and $A' = -A$ , then $A = -A$ .