Question

Prove that tr(A.A[sup]T[/sup])=tr(A[sup]T[/sup].A) for every matrix A.

Answer 1

Aij = A^Tji
tr(A.A^T) =∑ ∑A_ij A_ij = ∑ A_ij²
tr(A^T.A) =∑ ∑A_ji Aji = ∑ ∑A_ij Aij = ∑ A_ij²