Let $A =\left[ \begin{array} { c c c } { 4 } & { 0 } & { - 3 } \\ { 5 } & { 5 } & { - 4 } \end{array} \right]$, $B = \left[ \begin{array} { c c c } { - 5 } & { - 4 } & { 0 } \\ { 0 } & { 4 } & { 1 } \end{array} \right]$, and $C = \left[ \begin{array} { c c } { - 4 } & { - 2 } \\ { 0 } & { 5 } \\ { 5 } & { - 1 } \end{array} \right]$. Compute:

1. $A − 5B$ 

   Step (a):

   $\left[ \begin{array} { c c c } { 4-5(-5) } & { 0-5(-4) } & { -3-5(0) } \\ { 5-5(0) } & { 5-5(4) } & { - 4-5(1) } \end{array} \right]$

2. $AC − BC$ 

   Step (b):

   $BC = \left[ \begin{array} { c c } { -5(-4)-4(0)+0(5) } & { -5(-2)-4(5)+0(-1) } \\ { 0(-4)_4(0)+1(5) } & { 0(-2)+4(5)+1(-1) } \end{array} \right]$

3. $(BC)^2$ 

   Hint (c):

   Compute $(BC)(BC)$.
   $BC$ was computed in part (b).