Kunze Linear Algebra · Problem 1.6.7

Systems of Linear Equations

Mathematics — Methods · matrix-invertibility

Problem

Let AA be an n×nn \times n (square) matrix. Prove the following two statements: (a) If AA is invertible and AB=0AB = 0 for some n×nn \times n matrix BB, then B=0B = 0. (b) If AA is not invertible, then there exists an n×nn \times n matrix BB such that AB=0AB = 0 but B≠0B \neq 0.

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