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If A is symmetric as well as skew-symmet...

If A is symmetric as well as skew-symmetric matrix, then A is

A

diagonal matrix

B

null matrix

C

triangular materix

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let `A=[a_("ij")]`. Since a is skew-symmetric, we have
`a_(ii)=0` and `a_("ij")=-a_("ij") (i ne j)`
A is symmetric as well, so `a_("ij")=a_("ji")` for all `i` and `j`.
`:. A_("ij")=0` for all `i ne j`
Hence, `a_("ij")=0` for all `i` and `j`, i.e., A is a null matrix.
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