Mathematics 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.

Solve the following quadratic equation:

$x^2 - 5x + 6 = 0$

Find the values of x that satisfy this equation.

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