# Math Help - Linear Algebra - Self-adjoint...something something

1. ## Linear Algebra - Self-adjoint...something something

Let V be a finite dimensional inner product space. Show that the product of two self-adjoint linear maps S and T on V is self adjoint if and only if ST = TS

I have no idea what I am doing here.

2. Originally Posted by Chloroform
Let V be a finite dimensional inner product space. Show that the product of two self-adjoint linear maps S and T on V is self adjoint if and only if ST = TS.
The adjoint of a product is the product of the two adjoints in the opposite order. In other words, $(AB)^* = B^*A^*$. That's all you need to know in order to do this problem.