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Question

If A is a skew-symmetric matrix of order 3, then the matrix A4 is

A
skew symmetric
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B
symmetric
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C
diagonal
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D
none of those
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Solution

The correct option is B symmetric
We are given that the matrix A is skew symmetric which implies that,
AT=A --------(1)
(A4)T=(A.A.A.A.)T=ATATATAT (By applying the property of transpose of a matrix)
(-A) (-A) (-A) (-A) (Using equation (1))
=(1)4A4=A4
i.e,( A4)T=(A4)
A4 is symmetric.

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