Start by interchanging the top two rows:

Now subtract the top row from the bottom row:

That gets the first column to be what you want.

Multiply the middle row by –1:

Next, subtract the middle row from the top row, and subtract twice the middle row from the bottom row. That will get the second column to be what you want. After that, you just have to deal with the third column in a similar way, and you will have the answer.