Q. 485.0( 1 Vote )

If A, B are squar

Answer :

A matrix is said to be skew-symmetric if A = -A’


Given, B is a skew-symmetric matrix.


B = -B’


Let C = A’ BA …(1)


We have to prove C is skew-symmetric.


To prove: C = -C’


As C’ = (A’BA)’


We know that: (AB)’ = B’A’


C’ = (A’BA)’ = A’B’(A’)’


C’ = A’B’A { (A’)’ = A}


C’ = A’(-B)A


C’ = -A’BA …(2)


From equation 1 and 2:


We have,


C’ = -C


Thus we say that C = A’ BA is a skew-symmetric matrix.


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