My book doesn't solve it like a linear equation, they solve it by using inverse matrices.

Question

Solve the matrix equation:
|4 -5||m|=|32|
|1 2| |n|=|-5|

A= |4 -5|
|1 2|

X= |m|
|n|

B= |32|
|-5|

Step 1. Find the inverse of the coefficient matrix.

A^-1= 1/13|2 5|
|-1 4|

(I get confused in step 2)

Step 2. Multiply each side of the matrix by the inverse matrix

Answer 1

I am going to leave out the 1/13 on both sides of the matrix equation, so they line up nicely

│ 2 5││ 4-5││m│
│-1 4││ 1 2││n│ =

│ 2 5││32│
│-1 4││-5│

│13 0││m│
│0 13││n│ =

│ 39│
│-52│

so 13m=39 ----> m=3
and 13n=-52 --> n=-4