Question

show that A2 is symmetric ,if either AIs symmetric ​

Answer 1

Step-by-step explanation:

I first tried if the claim was true by testing it with a symmetric matrix, and I got that if I have a symmetric square matrix AA then A2A2 is also symmetric. So to prove this for a general case I did:

First of all I take a general square matrix A:

A=⎡⎣⎢⎢⎢a11a21...an1a12a12...an2...a1n...a1n......ann⎤⎦⎥⎥⎥A=[a11a12...a1na21a12...a1n.........an1an2...ann]

we can see that the matrix above is symmetric because it is equal to its transponse.

Then I calculate A2A2:

A2=⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢