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Question

If A is a symmetric matrix or skew symmetric matrix, then A2 is

A
an orthogonal matrix
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B
a symmetric matrix
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C
a unit matrix
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D
a diagonal matrix
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Solution

The correct option is B a symmetric matrix
A is a symmetric matrix,
then Aij=Aji

AT=A

If A is skew symmetric matrix
then
Aij=Aji
AT=A

(A2)T=(AT)2)=(A)2=A2 ( As AT=AorAT=A)

hence A2 is symmetric matrix.

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