Let A be an invertible $n \times n$ matrix whose inverse is itself. Prove that $\det(A)$ is either $1$ or $-1$. I’m really lost in class. I don’t even know where to start. Please help.
How can we prove that any bijection on any set is a composition of 2 involutions ? Since involutions are bijections mapping elements of a set to elements of the same set, I find it weird that this applies to any bijection. Thanks for your help !