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If A=\(\begin{bmatrix}a&b\\c&d\end{bmatrix}\), then which of the following is skew-symmetric?(a) AA’(b) A+A’(c) 2(A+A’)(d) A-A’The question was asked during an interview.Origin of the question is Symmetric and Skew Symmetric Matrices topic in chapter Matrices of Mathematics – Class 12

Answer»

The correct choice is (c) 2(A+A’)

To explain: GIVEN that, A=\(\begin{bmatrix}a&B\\c&d\end{bmatrix}\)

⇒A’=\(\begin{bmatrix}a&c\\b&d\end{bmatrix}\)

LET B=A-A’=\(\begin{bmatrix}a&b\\c&d\end{bmatrix}\)–\(\begin{bmatrix}a&c\\b&d\end{bmatrix}\)=\(\begin{bmatrix}a-a&b-c\\c-b&d-d\end{bmatrix}\)=\(\begin{bmatrix}0&b-c\\c-b&0\end{bmatrix}\)

B’=\(\begin{bmatrix}0&c-b\\b-c&0\end{bmatrix}\)=B’

THUS, B=A-A’ is a SKEW – symmetric.


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