Category: Algebra Exercises

Prove that diagonal elements of an antisymmetric matrix are zero.

Be $A,B$ and $C$ three matrices of order n. Proof that if $A$ commutes with $B$ and $A$ commutes with $C$, then $A$ commutes with the $BC$ .

Prove that diagonal elements of a Hermitian matrix are real.

Prove that the product of two upper triangular matrices is an upper triangular matrix.