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Question

If $$A$$ is symmetric as well as skew-symmetric matrix, then $$A$$ is


A
diagonal matrix
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B
null matrix
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C
triangular matrix
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D
none of these
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Solution

The correct option is B null matrix
Since, A is skew-symmetric.
$$A^{T}=-A$$
Since, A is symmetric.
$$A^{T}=A$$
$$\Rightarrow -A=A$$
$$\Rightarrow 2A=O$$
$$\Rightarrow A=O$$
Hence, A is a null matrix.

Mathematics

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