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(b) Suppose that A is a square matrix with the property that A³ = 0 (here "O" means the zero matrix of the same size as A). Prove that the matrix I + A is invertible, and that its inverse is given by (I + A)−¹ = I − A + A².

(b) Suppose that A is a square matrix with the property that A³ = 0 (here "O" means the zero matrix of the same size as A). Prove that the matrix I + A is invertible, and that its inverse is given by (I + A)−¹ = I − A + A².

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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(b) Suppose that A is a square matrix with the property that A³ = 0 (here "O" means the zero matrix of the same size as A). Prove that the matrix I + A is invertible, and that its inverse is given by (I + A)−¹ = I − A + A².
Transcribed Image Text:(b) Suppose that A is a square matrix with the property that A³ = 0 (here "O" means the zero matrix of the same size as A). Prove that the matrix I + A is invertible, and that its inverse is given by (I + A)−¹ = I − A + A².
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