How do you find the determinant of a matrix?

Finding the matrix of a matrix can be done in 5 steps. Step 1 involves finding the determinant of the matrix, and putting this value aside for later. Step 2 finds the cofactors of each element. The cofactor of an element 'a' is the determinant of the matrix created by removing the row and column that contain the element 'a' from the original matrix. For step 3 we need to replace each element with its cofactor. For a 2 by 2 matrix, step 2 and 3 essentially swaps each element with its diagonal. Now, for the 4th step we transpose the matrix, which is basically making the rows into columns. This is like reflecting the matrix along its leading diagonal. For the last step, we multiply this result by 1 over the determinant that we calculated in step 1, and we have our matrix inverse!