State whether the following statement is True or False:
If A is skew symmetric matrix, then A2 is a symmetric matrix.
A
False
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B
True
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Solution
The correct option is B True Given that A is skew symmetric ⇒A′=−A .... (1)
Now finding transpose of A2 ⇒(A2)′=2(A′)2 [∵(An)′=2(A′)n] ⇒(A2)′=(−A)2 [Using (1)] ⇒(A2)′=(A)2
[If A is symmetric matrix, then A′=A] ⇒A2is symmetric matrix.
Hence, the given statement is true.