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Let A and B be 2 x 2 matrices with real entries. Determine if the following statements are true or false. Justify your answer by either providing a short proof or a specific counter-example. (a) If det(A) = 0, then A is the zero matrix. (b) If det(AB) = 0, then det(A) = 0 or det(B) = 0. (c) det(A+ B) = det(A) + det(B). %3D (d) If A ER is a scalar, then det(AA) = A det(A).

Let A and B be 2 x 2 matrices with real entries. Determine if the following statements are true or false. Justify your answer by either providing a short proof or a specific counter-example. (a) If det(A) = 0, then A is the zero matrix. (b) If det(AB) = 0, then det(A) = 0 or det(B) = 0. (c) det(A+ B) = det(A) + det(B). %3D (d) If A ER is a scalar, then det(AA) = A det(A).

Advanced Engineering Mathematics
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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Let A and B be 2 x 2 matrices with real entries. Determine if the following statements are true or false. Justify your answer by either providing a short proof or a specific counter-example. (a) If det(A) = 0, then A is the zero matrix. (b) If det(AB) = 0, then det(A) = 0 or det(B) = 0. (c) det(A+ B) = det(A) + det(B). (d) If A e R is a scalar, then det(AA) = A det(A).
Transcribed Image Text:Let A and B be 2 x 2 matrices with real entries. Determine if the following statements are true or false. Justify your answer by either providing a short proof or a specific counter-example. (a) If det(A) = 0, then A is the zero matrix. (b) If det(AB) = 0, then det(A) = 0 or det(B) = 0. (c) det(A+ B) = det(A) + det(B). (d) If A e R is a scalar, then det(AA) = A det(A).
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