Proving Symmetry of (A)(A^T) Matrix w/ Tensor Notation

[neelakash]

Homework Statement

We are to show that (A)(A^T) is a symmetric matrix using tensor notation.

Where ^T denotes TRANSPOSE

Homework Equations

The Attempt at a Solution

I did it in the following way:
Let P=(A)(A^T)
Then,
p_ik=(a_ij)(a_jk) Where A=a_ij and A^T=a_jk
=(a_jk^T)(a_ji)
=(a_kj)(a_ji)
=p_ki

hence proved.
Please tell if I am correct.

 

[EnumaElish]

It seems right.