Question

Prove that for any matrix A ,
AA^t is a symmetric matrix, also A^tA

Answer 1

Since AAt is symmetric, AAt=(AAt)t=At Att=At A......(1)
Now (At A)t= Att At = A At=At A, by (1)
Hence At A is symmetric

Answer 2

You 've to prove that both AA^t , A^tA are symmetric for any matrix A

Answer 3

oh use the property (AB)t=Bt At
see (AAt)t=Att At= AAt
This shows that AAt is symmetric

Answer 4

also (At A)t=At Att=At A
this shows that At A is symmetric

Answer 5

Thanks a lot :)

Answer 6

I didn't think of transposing it xD