To find the determinant of a 3*3 matrix, we use the method of cofactor expansion. This involves multiplying each element of a row (or column) by its cofactor, which is the determinant of the 2*2 matrix obtained by deleting the row and column of that element. You calculate the 2*2 determinants inside each term, and then multiply them by the respective elements. The signs alternate (positive, negative, positive) based on the position of the element. This process gives you the determinant of the matrix.