Find the inverse of a 3x3 matrix

There are 4 key steps to this question.

(i) calculate the matrix of minors: you want to find the determinant of each entry and this forms a new matrix. 

(ii) convert this into a matrix of cofactors: this is a 'checkerboard' of minuses that you apply to the matrix of minors, i.e. change the sign of alternate cells.

(iii) find the adjugate/adjoint: transpose all elements of the matrix of cofactors i.e. swap all positions of entries over the diagonal

(iv) multiply by 1/determinant: find the determinat of the original matrix. We have already calculated the determinants of the smaller parts in the first part of the question. To find the determinant, you multiply the top row elements by their 'minor' determinants. 

Best explained through a working example on a whiteboard. This question often carries a lot of marks in an exam paper, and the maths itself is not complex but it is very easy to make a mistake.