if A&B are symentric matrices of the same order then show AB is symentric if and only if AB=BA
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Hey there!
Here's the answer you are looking for!
Since AB is symmetric, we have
AB = (AB)^T(AB)
T
But (AB)^T(AB)
T
= B^TB
T
A^TA
T
Hence, AB = B^TB
T
A^TA
T
------(1)
It is also given that A and B are symmetric.
Hence by --(1) becomes,
AB = BA
Thus, AB is symmetric if and only if AB = BA.
HOPE IT HELPS ^_^
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