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.

Exclude leap years from the following calculations. (a) compute the probability that a randomly selected person does not have a birthday on october 4. (type an integer or a decimal rounded to three decimal places as needed.) (b) compute the probability that a randomly selected person does not have a birthday on the 1st day of a month. (type an integer or a decimal rounded to three decimal places as needed.) (c) compute the probability that a randomly selected person does not have a birthday on the 30th day of a month. (type an integer or a decimal rounded to three decimal places as needed.) (d) compute the probability that a randomly selected person was not born in january. (type an integer or a decimal rounded to three decimal places as needed.)