I was reading the book "Linear Representations of Finite Groups" by Jean-Pierre Serre, and in the begining of the chapter 2.4 about decomposition of the regular representation he states that
The character $X_{reg}(g)$ of the regular representation satisfies: $X_{reg}(g)=\begin{cases}\mid G\mid&g=1_G\\0&\text{otherwise}\end{cases}$
But i don't get why this is true. I'm having trouble making the matrix form of the regular representation and i think that it will will help me understand why this needs to be true.