The Cofactor Expansion

You'll often need to find the determinant of a matrix. For a 2 by 2 matrix, you can use this formula, but for bigger matrices, this will not work.

The cofactor expansion works for any square matrix, which are the only ones that have determinants. Let's see how it works.

The Checkerboard

If you remember only just this checkboard, you can still have a good idea of how to do the cofactor expansion.

The Technique

You can expand the section below to see a textual description of how to do the cofactor expansion; however, I believe you'll find it more intuitive to just watch the animation instead.

The details...

Start off by choosing any column or row to expand along. Zeroes are very simple to expand; if you find them, expand along them.

For each element along the row or column, ignore all elements that share a vertical or horizontal line with it. We only care about the element we're expanding, the off-axis elements, and remember that checkerboard? We'll also want the sign that corresponds to our element we're expanding.

You should now have a sub-matrix, one isolated element, and the corresponding sign from the checkerboard. Multiply these all together.

When you add up all the expansions along one row or column, the result is the determinant.

Confused? Have a look at the animation below.