### Home > PC3 > Chapter 9 > Lesson 9.1.3 > Problem9-53

9-53.

​What matrix can you multiply by $M=\begin{bmatrix} { 2 } & { 1 } \\ { 4 } & { 0 } \end{bmatrix}$ to get a result of $\left[ \begin{array} { l l } { 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right]$?

$\begin{bmatrix} { 2 } & { 1 } \\ { 4 } & { 0 } \end{bmatrix} \begin{bmatrix} { a } & { b } \\ { c } & { d } \end{bmatrix} =\begin{bmatrix} { 1 } & { 0 } \\ { 0 } & { 1 } \end{bmatrix}$

Solve the system:
$2a + 1c = 1\\4a +0c=0$

Repeat the process in step 2 for the rows of $M$ multiplied by the $b-d$ column.