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Matrix

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If $A$ and $B$ are symmetric matrices of the same order, then $AB-BA$ is

  1. NULL matrix
  2. Symmetric matrix
  3. Skew symmetric matrix
  4. Orthogonal matrix

1 Answer

0 0 votes
A = A'
B = B'

(AB - BA)' = [(AB)' - (BA)'] = B'A' - A'B'.....................(1)

And, from the question..!!
AB - BA = A'B' - B'A'.....{Substituting A=A', and B=B'}....................(2)

So, from 1 and 2....

(AB - BA) = -(AB - BA)'  
Hence, AB - BA is skew Symmetric..!!
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