Determinant proof question. 
Using determinants, prove that if $A_1,A_2,...,A_m$ are invertible $nxn$ matrices, where $m$ is a positive integer, then $A_1A_2...A_m$ is an invertible matrix.

Need help starting the proof. Do I show that $A_1,A_2,..,A_m$'s determinant is not equal to zero and use the determinant property, $det(AB)=det(A)det(B)$.  Not sure where to go from here.

A matrix is invertible if and only if its determinant is nonzero. Since $\det(A_i)\neq 0$, and $\det(A_1...A_n)=\det(A_1)...\det(A_n)$, we know that $\det(A_1...A_n)\neq 0$, so $A_1...A_n$ is invertible.
