Exercise 15 Page 202

We want to determine if P and Q are inverse matrices. P= [ cc 4 & 0 3 & 0 ] Q= [ cc -1 & -1 23 & 5 ]Two matrices are inverses of each other if their product is the identity matrix. MatricesA andB are inverses ⇕ A * B = B * A = I, where I= [ cc 1 & 0 0 & 1 ] Recall that the Commutative Property of Multiplication does not hold for matrices. Therefore, for P and Q to be inverses, both P* Q and Q* P have to equal the identity matrix. Let's start by calculating P* Q.

Since P* Q ≠ I, we do not need to check if Q* P is equal to I. We already know that matrices P and Q are not inverses.