Question #6013

if B is skew symmetric matrix,write whether (AB'A) is skew symmetric or symmetric matrix.

Expert's answer

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.

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.

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