Mathematics

Problem

Consider the matrices

A=\begin{pmatrix}4&3\\3&2\end{pmatrix},\qquad B=\begin{pmatrix}-2&3\\3&k\end{pmatrix},

where

k

is a real number. a. (i) Determine the value of

k

for which

AB=I_2

, where

I_2

is the

2\times2

identity matrix. b. (ii) For the value of

k

obtained in (i), compute

BA

. c. (iii) What conclusion can you draw about the relationship between

A

and

B

? Justify with reference to your calculations.