Question

if ATA is symmetric then PT=(AT)2​

Answer 1

Explanation:

Given A be a square matrix.

Let, B=A−A

T

.

Now,

B

T

=A

T

−(A

T

)

T

=A

T

−A

=−(A−A

T

)

=−B.

As B

T

=−B then B i.e. A−A

T

is a skew-symmetric matrix.