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# If A and B are skew symmetric matrices,then prove that ABA is skew symmetric.

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• A square matrix A=$[a_{ij}]$ is said to be skew symmetric if A'=-A.
• (i.e) $[a_{ij}]=-[a_{ji}]$ for all possible value of i & j.
A'=-A.
B'=-B.
[(AB)A]'=A'(AB)'
$\qquad\;\;\;\;=A'(B'A')$
Replace A'=-A & B'=-B.
$\Rightarrow (-A)(-B)(-A)$
$\Rightarrow -(ABA).$
Hence ABA is skew symmetric.