Assume A is nonsingular. Prove that det(A-1) 1 det(A) Let c be any scalar. Prove that det(cA) = c" det(A).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 11E
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4. Let A be any n × n matrix.

Prove each of the two statements with its given information:

 

Assume A is nonsingular. Prove that det(A-1) =
det (A)
Let c be any scalar. Prove that det(cA) = c" det(A).
Transcribed Image Text:Assume A is nonsingular. Prove that det(A-1) = det (A) Let c be any scalar. Prove that det(cA) = c" det(A).
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