Inverse matrices are like inverses for numbers:
A A-1 = A-1 A = INote that .
The inverse only exists when the determinant of the matrix, |A|, is nonzero.
To get the inverses of small matrices, you could use the procedure of taking ``minors''. In index notation:
where Aij is the matrix A after you remove the column and row of element aij. See the example problems.
(AB)-1 = B-1 A-1
Transposing and inversing commute: