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Consider square matrices A & B where A#0, B#0,AB=0. Show that |A|=0 or |B|=0.

Consider square matrices A & B where A#0, B#0,AB=0. Show that |A|=0 or |B|=0.

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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### Problem Statement Consider square matrices \( A \) and \( B \) where: 1. \( A \neq 0 \) 2. \( B \neq 0 \) 3. \( AB = 0 \) Show that \( |A| = 0 \) or \( |B| = 0 \). ### Explanation This problem requires us to demonstrate that if the product of two non-zero square matrices results in the zero matrix, then at least one of the matrices must have a determinant equal to zero, indicating that it is singular.
Transcribed Image Text:### Problem Statement Consider square matrices \( A \) and \( B \) where: 1. \( A \neq 0 \) 2. \( B \neq 0 \) 3. \( AB = 0 \) Show that \( |A| = 0 \) or \( |B| = 0 \). ### Explanation This problem requires us to demonstrate that if the product of two non-zero square matrices results in the zero matrix, then at least one of the matrices must have a determinant equal to zero, indicating that it is singular.
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