Answer to Question #197116 in Linear Algebra for Stefanus Weyulu

Question

Prove that if A, B, and C are n × n non-singular matrices, then (ABC)^-1 = C^−1B^−1A^−1 .

Answer 1

$(ABC)^{-1}=[(AB)C]^{-1}=C^{-1}(AB)^{-1}=C^{-1}B^{-1}A^{-1}$