The matrices C= pmatrix 1&1 0&1 pmatrix , D= pmatrix 1&-1 0&1 pmatrix are given.

MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

The matrices

C=\begin{pmatrix}1&1\\0&1\end{pmatrix},\qquad D=\begin{pmatrix}1&-1\\0&1\end{pmatrix}

are given. (i) Calculate the product

CD

. (ii) Calculate the product

DC

. (iii) From your answers to (i) and (ii), decide whether

C

and

D

are inverses of each other. Give a reason for your decision.