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Prove: Suppose A, B, C are square matrices. (a) if AB = 0, and A is invertible, then B = 0 the zero matrix. (b) if AB = AC, and A is invertible, then B = C. Hint for both: no need to look at the entries of the matrices. Also be careful if you apply an inverse.

Prove: Suppose A, B, C are square matrices. (a) if AB = 0, and A is invertible, then B = 0 the zero matrix. (b) if AB = AC, and A is invertible, then B = C. Hint for both: no need to look at the entries of the matrices. Also be careful if you apply an inverse.

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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1. Prove: Suppose A, B, C are square matrices. (a) if AB = 0, and A is invertible, then B = 0 the zero matrix. (b) if AB = AC, and A is invertible, then B = C. Hint for both: no need to look at the entries of the matrices. Also be careful if you apply an inverse.
Transcribed Image Text:1. Prove: Suppose A, B, C are square matrices. (a) if AB = 0, and A is invertible, then B = 0 the zero matrix. (b) if AB = AC, and A is invertible, then B = C. Hint for both: no need to look at the entries of the matrices. Also be careful if you apply an inverse.
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