Question
If A is a skew-symmetric matrix of order 3, then the matrix A4 is
Answer: Option B
:
B
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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B
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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