Exercise 16 Page 202

We want to determine if R and S are inverse matrices. R= [ cc 12 & - 14 14 & - 12 ] S= [ cc 2 & 4 4 & 2 ]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 R and S to be inverses, both R* S and S* R have to equal the identity matrix. Let's start by calculating R* S.

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