Mathematics: Suppose that a and b are square matrices and that abc is invertible. show that each of a, b, and c is invertible.

Suppose that a and b are square matrices and that

Ответ:

deedivinya

02.01.2022

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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Ответ:

logicalness243

30.11.2022

Mathematics

-(1/2)

Step-by-step explanation:

y1-y2/x1-x2

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Suppose that a and b are square matrices and that abc is invertible. show that each of a, b, and c is invertible.

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