Let A be an n x n matrix such that A3 = In. (a) Is A invertible? If so, what is A-1? If not, explain why. (b) What conclusions can you make, if any, about the rank and determinant of A?
Let A be an n x n matrix such that A3 = In. (a) Is A invertible? If so, what is A-1? If not, explain why. (b) What conclusions can you make, if any, about the rank and determinant of A?
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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Transcribed Image Text:3. Let A be an n x n matrix such that A3 = In.
(a) Is A invertible? If so, what is A-1? If not, explain why.
(b) What conclusions can you make, if any, about the rank and determinant of A?
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