Inverse of a Matrix: Solve for m, n, p

m+2n+p=5

3m+4n+p=8

m-6n+2p=4

There are 2 ways taught us to solve for this using matrix.

The Inverse method and Row-Echelon method.

In row echelon method i got this answer:

m=1

n=1/2

p=3

i know the answer is correct because when i substitute it to the equations above, i get the correct answer.

(1)+2(1/2)+(3)=5

3(1)+4(1/2)+(3)=8

1-6(1/2)+2(3)=4

My problem is, when I use the Inverse method, i get the determinant -18, and the rest of the process gives me a wrong answer.