If A and B are matrices of same order then (AB'

Engineering

Mathematics

Special Type of Square Matrices

Symmetric and Skew Symmetric Matrices

Question

If A and B are matrices of same order then (AB' – BA') is a

skew symmetric matrix

null matrix

symmetric matrix

unit matrix

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We have matrices A and B of same order.
Let P = (AB' – BA')
Then, P' = (AB' – BA')' = (AB')' – (BA')'

= (B')'(A)' – (A')'B' = BA' – AB' ⋯⋯⋅ {∵ (MN)' = N'M'}

= – (AB' – BA') = – P ....... {∵ (A')' = A}

Hence, (AB – BA') is a skew symmetric matrix.