In multiplying two real numbers, we are familiar with the so-called “Zero-Product Property” from both Intermediate and College Algebra. Recall that this says that if you have two numbers x and y such that the product xy = 0, then either x = 0, y = 0 or they are both zero. Can the same be said of matrices? In other words, given matrices A and B where AB = 0, does that mean that either A = 0, or B = 0 or both (where 0 denotes the zero matrix here).
Let A= 3 −6
−1 2
Try to construct a 2 × 2 matrix B such that AB is the zero matrix (make sure you clearly show the multiplication). Use two different nonzero columns for B.