Answer
See below
Work Step by Step
For matrices $A_1,A_2$ we know $(A_1A_2)^{-1}=A_2^{-1}A_1^{-1}$
For $A_1,A_2,A_3$ first we need to let $A_1A_2=B_2$ then
$(A_1A_2A_3)^{-1}\\
=(B_2A_3)^{-1}\\=A_3^{-1}B_2^{-1}\\=A_3^{-1}A_2^{-1}A_1^{-1}$
For $n$ matrices,matrices then we have $(A_1A_2...A_n)^{-1}\\
=A_n^{-1}...A_2^{-1}A_1^{-1}$
For $n+1$ first we let $B_n=A_1A_2...A_n$, then:
$(A_1A_2...A_nA_{n+1})^{-1}\\
=(B_n.A_{n+1})^{-1}\\=A_{n+1}^{-1}B^{-1}_n\\=A_{n+1}^{-1}A_n^{-1}...A_2^{-1}A_1^{-1}$
