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Let A and B be two square matrices of order n over a fiéid F and AEF Then (I) tr (AA)=d Ir A; (2) Ir (A+B)=fr A+ tr B; (3) tr (AB)=tr (BA).

Let A and B be two square matrices of order n over a fiéid F and AEF Then (I) tr (AA)=d Ir A; (2) Ir (A+B)=fr A+ tr B; (3) tr (AB)=tr (BA).

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 two square matrices of order n over a fiéid F and dEF Then (I) Ir (AA)=À Ir A; {2) Ir (A+B)=ir A+tr B; (3) tr (AB)=1r (BA).
Transcribed Image Text:Let A and B be two square matrices of order n over a fiéid F and dEF Then (I) Ir (AA)=À Ir A; {2) Ir (A+B)=ir A+tr B; (3) tr (AB)=1r (BA).
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