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CBSE Class 12-science Answered

if A and B are square matrices of same order show that AB^T-BA^T is skew symmetric matrix
Asked by sukumar.p | 10 Feb, 2018, 09:01: PM
answered-by-expert Expert Answer
Consider any two distinct matrices of order 2 or 3 
find AB and BA also find transpose of both. 
Now find transpose AB - transpose of BA you will get matrix show that transpose of that matrix is multiplied by minus sign of original matrix. Hence it is a skwe symmetric matrix.
Answered by Sneha shidid | 11 Feb, 2018, 01:03: PM

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  begin mathsize 12px style If space straight A to the power of straight T space equals space open square brackets table row 1 cell negative 1 end cell 2 row 4 3 cell negative 2 end cell end table close square brackets space space and space space straight B space equals space open square brackets table row 2 cell negative 3 end cell row 1 cell negative 4 end cell row 2 cell negative 2 end cell end table close square brackets space then space show space that space open parentheses straight A space plus space straight B close parentheses to the power of straight T space equals space straight A to the power of straight T space end exponent plus space straight B to the power of straight T end style
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