Determinant of 4x4 Matrix: Is the Method Used in the Video Accurate?

[ZedCar]

Homework Statement

I was using the method shown in the following video;


to find the determinant for the following 4x4 matrix

1 -2 3 -4
5 6 -7 8
-9 -10 11 -12
-13 14 -15 16

The Attempt at a Solution

I was therefore expanding this out by using the first three columns set to the right of this matrix.

Is this the correct thing to do if using this method?

I get an answer of -3264

Though when I use this online determinant calculator
http://www.bluebit.gr/matrix-calculator/
it provides an answer of 0

 

[ZedCar]

Apparently this method simply doesn't work for a 4x4 matrix.
And I've been told the correct answer is zero.

Just that our lecturer stated when finding the determinant using this method;

nxn determinant
add n-1 columns

So I thought by this he meant doing what I had done above.