Let A and B be n x n matrices such that det(A) 0 and det(B) + 0. Consider the following statements. Based on the properties of determinants which of the following is false? O det(AB) = det(A) + det(B) O det(AB) = det(BA) O det ((AB)-1) 1 det(A)det(B) O det(A" B") = det(AB) O If A = -B then det(A) = (-1)"det(B) %3D
Let A and B be n x n matrices such that det(A) 0 and det(B) + 0. Consider the following statements. Based on the properties of determinants which of the following is false? O det(AB) = det(A) + det(B) O det(AB) = det(BA) O det ((AB)-1) 1 det(A)det(B) O det(A" B") = det(AB) O If A = -B then det(A) = (-1)"det(B) %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let A and B be n x n matrices such that
det (A) # 0 and det(B) + 0. Consider the
following statements. Based on the properties of
determinants which of the following is false?
O det (AB) = det(A) + det(B)
O det (AB) = det(BA)
O det ((AB)-1) =
1
det(A)det(B)
O det(A" BT) = det(AB)
O If A = -B then det (A) = (-1)"det(B)
%3D
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