Answer to Question #6013 in Matrix | Tensor Analysis for soniya
if B is skew symmetric matrix,write whether (AB'A) is skew symmetric or symmetric matrix.
if B is skew symmetric matrix, then B' is a skew symmetric matrix.
AB'A isn neither skew symmetric nor symmetric matrix in general case.
We can ensure this by taking
B = ( 0 -1 )
& ( 1& 0 ),
A = ( 1 2 )
& & ( 3 4 ),
for example. We'll get
AB'A = ( 1 0 )
& ( 5 4 ).
This example shows that this statement is not correct in general, it's a refutation.