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Adjoint of a Matrix

If A is a rea...

Question

If A is a real square matrix , then $A A^{T}$ is

A

Unsymmetric

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B

Always symmetric

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C

Skew symmetric

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D

Sometimes symmetric

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Solution

The correct option is B Always symmetric
$(A A^{T})^{T} = (A T)^{T} A^{T} = A A^{T}$
$\Rightarrow A A^{T} i s a l w a y s s y m m e t r i c$

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