What would be the best way to find the inverse of this matrix?

A=

[1 3 0 -1]

[-3 -5 -8 3]

[-4 -12 6 4]

[0 -1 2 1]

I have been told to use the I method using the matrix

I=

[1000]

[0100]

[0010]

[0001]

By performing the row reductions on A to transform into I, along the way doing the same row reductions to I in order to find the inverse?

This seems to be more complicated than it has to be, any insights or ideas as to how I should approach this question