1 Answer

Chrisli · Answer 1 · 2020-02-06T02:02:48+0000

Answer:

Explanation:

Let A, B and C be square matrices, let
D = ABC . Suppose also that D is an invertible square matrix. Since D is an invertible matrix, then
$det (D) \\eq 0$ . Now,
$det (D) = det (ABC) = det (A) det (B) det (C) \\eq 0$ . Therefore,

$det (A) \\eq 0$

$det (B) \\eq 0$

$det (C) \\eq 0$

which proves that A, B and C are invertible square matrices.

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