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Question

If A is a square matrix, then which of the following is correct ?

(a) AAT is symmetric matrix and ATA is skew-symmetric matrix.
(b) AAT is skew-symmetric matrix and ATA is symmetric matrix.
(c) Both AAT and ATA are symmetric matrices.
(d) Both AAT and ATA are skew-symmetric matrices.

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Solution

We have

(AAT)T=((AT)TAT)=AAT [(AT)T=A]

AAT is symmetric matrix.

(ATA)T=(AT(AT)T)=ATA

ATA is symmetric matrix.


Option (c) is correct.


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