### Home > PC > Chapter 12 > Lesson 12.1.1 > Problem12-9

12-9.

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. Find $MN$.

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

2. Find values for $a, b, c,$ and $d$ so that $MN = I$?

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

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 $M^{–1}$.