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If the matrix A is both symmetric and skew symmetric, then

Question

If the matrix $A$ is both symmetric and skew symmetric, then

A

is a diagonal matrix

A

is a zero matrix

A

is a square matrix

None of these

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If the matrix

A

is both symmetric and skew symmetric, then

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Text solutionVerified

A

is both symmetric and skew symmetric, then we should have

A^{'} = A

and

A^{'} = - A

\Rightarrow A = - A

\Rightarrow A + A = 0

\Rightarrow 2 A = 0

\Rightarrow A = 0

Therefore,

A

is a zero matrix.

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Question Text	If the matrix $A$ is both symmetric and skew symmetric, then
Answer Type	Text solution:1
Upvotes	150