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# If A and B are symmetric matrices,then $\quad AB-BA\;is\;a\;\text{_______}$

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## 1 Answer

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Toolbox:
• A square matrix A=[a$_{ij}$] is said to be skew symmetric if A'=-A that is $[a_{ij}]= -[a_{ji}]$ for all possible value of i and j.
• A square matrix A=[a$_{ij}$] is said to be symmetric if A'=A that is $[a_{ij}]=[a_{ji}]$ for all possible value of i and j.
Given
A and B are symmetric matrices
$\rightarrow$ A=A'
$\rightarrow$B=B'
AB-BA is a skew symmetric matrix.
answered Apr 4, 2013

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