The determinant of 2 by 2 matrix can be worked out almost instantly:

ie multiply the diagonal numbers together and subtract them.

The determinant of a 3 by 3 matrix is much more difficult. We have to carry out a process called expanding along a row or a column, In the example below I will expand along a row – the top row.

Example:

We label the positions in the matrix with +1's and -1's: For the first term, 3, cross out the entries in the same row and column as this 3.

Our second term is

Our third term is

The determinant is