Algebra II (Matrices)

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

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

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  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

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