Prove that if B is the matrix obtained by interchanging the rows of a 2 ×2 matrix A, then det(B) = −det(A).

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.1: Operations With Matrices
Problem 76E
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Prove that if B is the matrix obtained by interchanging the rows of a 2 ×2 matrix A, then det(B) = −det(A).

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