Can someone explain to me the following step by step , i 've looked in websites , plus the book and i want to understand how this problem has this answer.

Question

Problem #1

Find the inverse if it exists, for the matrix.

-2_1_3
3_-1_0
-4_2_0

Answer is:
-4_6_5
-8_12_13
2__0__-1

sorry the problem posted up twice

To find the multiplicative inverse, you can use this form:

-2..1..3..|..1..0..0
.3.-1..0..|..0..1..0
-4..2..0..|..0..0..1

The objective is to get the left side to look like the right side, and the multiplicative inverse will be on the right side when finished. Whatever operations you do to the left side, you need to do to the right side as well.

Here's a few basic row operations:
1. Any 2 rows can be interchanged.
2. Any row can be multiplied by a number other than zero.
3. Any row can be replaced by adding a multiple of another row plus that row.

If the answer is as you stated, you should end up with this:

1..0..0..|.-4..6..5
0..1..0..|.-8.12.13
0..0..1..|..2..0.-1

I haven't worked this out, so I hope this will help get you started.