How do you find the determinant of this four by four matrices by using ellimination?

MY MATRICES:

0 -2 3 -4
-5 -6 7 -8
9 -10 11 -12
13 -14 -15 16

P.S I know how to find the determinant of a three by three and a two by two easily using ellimination, but struggle with a four by four.

THANK YOU FOR YOUR TIME!

It is tedious to do these things by hand. In my opinion, it has become rather anachronistic to do these manually when calculators will do them lickety-split. The important thing is knowing when to use a det. Let a calculator do the grunt work. One can use cofactors. Or, using row reduction methods, turn the matrix into a upper or lower triangular matrix and bring out common factors to multiply.

I will tell you the determinant is -2128.

There is something to shoot for if you want to give it a go.

There are some det laws that are helpful to know.

Here is an example of what I mean.



Interchange first and second rows:



Remove a common factor of 3 from the first row:



-2 times first row added to third row:



-10 times second row added to third row:



Remove a common factor of -55 from the last row: