Let $M=\left[ \begin{array} { c c } { 1 } & { 0 } \\ { - 1 } & { 2 } \end{array} \right]$ and $N = \left[ \begin{array} { l l } { a } & { b } \\ { c } & { d } \end{array} \right]$.  

1. Calculate $MN$.

    Step (a):

   $\left[ \begin{array} { c c } { 1(a)+0(c) } & { 1(b)+0(d0 } \\ { - 1(a)+2(c) } & { -1(b)+2(d) } \end{array} \right]$

2. For what values of $a, b, c,$ and $d$ does $MN = I$?

   Hint (b):

   $I =\left[ \begin{array} { c c } { 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right]$

    Step (b):

   Using the lower left entry from part (a) and matrix $I$:
   $−1(a) + 2(c) = 0$
   Now repeat this process for the rest of the entries.

3. Use the results of part (b) to write the matrix $M^{–1}$.