Mathematics

Problem

The matrices

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

are given. a. (i) Calculate the product

CD

. b. (ii) Calculate the product

DC

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

C

and

D

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