(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.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter3: Matrices
Section3.5: Subspaces, Basis, Dimension, And Rank
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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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