5. (an) is diagonal nxn matrix. (1) Show that A is invertible <> none of the ai's is zero. alar. 0 A = a (2) If A is invertible, what is the inverse of A ? 6. A is an invertible matrix. (1) If A+B is invertible, show that I + BA is also invertible. (2) If A+B is not invertible, show that I+ BA is not invertible either

5. (an) is diagonal nxn matrix. (1) Show that A is invertible <> none of the ai's is zero. alar. 0 A = a (2) If A is invertible, what is the inverse of A ? 6. A is an invertible matrix. (1) If A+B is invertible, show that I + BA is also invertible. (2) If A+B is not invertible, show that I+ BA is not invertible either

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.CR: Review Exercises

Problem 37CR

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