Triangle geometry/Law of cosines/Fact/Proof/Exercise

Let a triangle ${\displaystyle {}(A,B,C)}$ be given, with side lengths ${\displaystyle {}a,b,c}$. Let ${\displaystyle {}\gamma }$ denote the angle at ${\displaystyle {}C}$. Show that

${\displaystyle {}c^{2}=a^{2}+b^{2}-2ab\cos \gamma \,}$

holds.