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vitfil [10]
4 years ago
15

Suppose that A and B are square matrices and that ABC is invertible. Show that each of A, B, and C is invertible.

Mathematics
1 answer:
Dimas [21]4 years ago
8 0

Answer:

Step-by-step 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) \neq 0. Now, det (D) = det (ABC) = det (A) det (B) det (C) \neq 0. Therefore,

det (A) \neq 0

det (B) \neq 0

det (C) \neq 0

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

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