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Q14.    If the matrix A is both symmetric and skew-symmetric, then

            (A) A is a diagonal matrix
            (B) A is a zero matrix
            (C) A is a square matrix
            (D) None of these

 

Answers (1)

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

A'=A                  and     A'=-A

         A'=A'

\Rightarrow \, \, \, \, \, \, \, A=-A

\Rightarrow \, \, \, \, \, \, \, A+A=0

\Rightarrow \, \, \, \, \, \, \, 2A=0

\Rightarrow \, \, \, \, \, \, \, A=0

Hence, A is a zero matrix.

Option B is correct.

 

Posted by

seema garhwal

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