Math, asked by 19se16gurukiranl, 9 months ago

if A&B are symentric matrices of the same order then show AB is symentric if and only if AB=BA​

Answers

Answered by brainlyboy1248
2

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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