Mathematics

Problem

The

2\times 2

matrices

A

and

B

are given by

A=\begin{pmatrix}1&2\\3&4\end{pmatrix},\quad B=\begin{pmatrix}0&1\\2&3\end{pmatrix},

and

I_{2}

denotes the

2\times 2

identity matrix. a. Simplify and calculate the matrix

S=2(A+B)-3B+4I_{2}

. b. Show that

2(A+B)-3B=2A-B

and confirm this equality with the given matrices. c. Find the trace of the matrix

S

obtained in part (i).