Answer:
Step-by-step explanation:
Let A, B and C be square matrices, let [tex]D = ABC[/tex]. Suppose also that D is an invertible square matrix. Since D is an invertible matrix, then [tex]det (D) \neq 0[/tex]. Now, [tex]det (D) = det (ABC) = det (A) det (B) det (C) \neq 0[/tex]. Therefore,
[tex]det (A) \neq 0[/tex]
[tex]det (B) \neq 0 [/tex]
[tex]det (C) \neq 0[/tex]
which proves that A, B and C are invertible square matrices.
