Prove that if M e Mnxn(F) can be written in the…

Prove that if M e Mnxn(F) can be written in the form M = (6 2). (A B' %3D where A and C are square matrices, then det(M) = det(A). det(C).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 33E

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Question

Prove that if M e Mnxn(F) can be written in the form
M = (6 2).
(A B'
%3D
where A and C are square matrices, then det(M) = det(A). det(C).

Expert Solution