1 2 3 5. (a) Find the inverse of the matrix A = 2 4 5 As always, show your work. 3 5 6 (b) Suppose that B is an n x n matrix such that B²+B = I. Is B necessarily invertible? Justify your answer.

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.5: Determinants
Problem 82E: Use an example chosen from 22 matrices to show that for nn matrices A and B,ABBA but AB=BA.
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1 2 3
5. (a) Find the inverse of the matrix A
2 4 5
As always, show your work.
3 5 6
(b) Suppose that B is an n × n matrix such that B²+B = I. Is B necessarily
invertible? Justify your answer.
Transcribed Image Text:1 2 3 5. (a) Find the inverse of the matrix A 2 4 5 As always, show your work. 3 5 6 (b) Suppose that B is an n × n matrix such that B²+B = I. Is B necessarily invertible? Justify your answer.
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