Determinants of Matrices

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. 


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