9. Let A € M (R) such that I + A is invertible. Suppose that B= (1 - A) (I + A)-1 (a) Show that B = (1 + A)-'(I - A) (b) Show that I + B is invertible and express A in terms of B.

匿名用户最后更新于 2021-12-01 19:08 数学类Mathematics

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9. Let A € M (R) such that I + A is invertible. Suppose that B= (1 - A) (I + A)-1 (a) Show that B = (1 + A)-&#x27;(I - A) (b) Show that I + B is invertible and express A in terms of B.

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9. Let A € M (R) such that I + A is invertible. Suppose that B= (1 - A) (I + A)-1 (a) Show that B = (1 + A)-'(I - A) (b) Show that I + B is invertible and express A in terms of B.