Q. 214.0( 4 Votes )

If the matrix A is both symmetric and skew-symmetric, show that A is a zero matrix.

Answer :

Given that matrix A is both symmetric and skew symmetric, then,


We have A = A’ ……(i)


And A = -A’ ……(ii)


From (i) and (ii) we get,


A’ = -A’,


2A’ = 0


A’ = 0


Then, A = 0


Hence proved.


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