Which of the followings are always true? 1. A? = I implies that det(A) = 1 II. If A and B are upper triangular matrices then AB=BA. III. If det(A) = 1 then adj(adj(A)) = A IV. Given any two matrices A and B, det(AB)=det(A).det(B) V. If A is nxn matrix then det(kA) = k" det(A) O I,V O I,IV,V O II,V O 1,II,V

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.4: Similarity And Diagonalization
Problem 40EQ
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Which of the followings are always true?
I. A2 = I implies that det(A) = 1
II. If A and B are upper triangular matrices then AB=BA.
II. If det(A) = 1 then adj(adj(A)) = A
IV. Given any two matrices A and B, det(AB)=Ddet(A).det(B)
V. If A is nxn matrix then det(kA) = k" det(A)
O I,V
O III,IV,V
O I,V
Transcribed Image Text:Which of the followings are always true? I. A2 = I implies that det(A) = 1 II. If A and B are upper triangular matrices then AB=BA. II. If det(A) = 1 then adj(adj(A)) = A IV. Given any two matrices A and B, det(AB)=Ddet(A).det(B) V. If A is nxn matrix then det(kA) = k" det(A) O I,V O III,IV,V O I,V
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