16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 1.6.7
Systems of Linear Equations
Mathematics — Linear Algebra · matrix-invertibility
Problem
Let A be an n×n (square) matrix. Prove the following two statements:
(a) If A is invertible and AB=0 for some n×n matrix B, then B=0.
(b) If A is not invertible, then there exists an n×n matrix B such that AB=0 but B=0.