Matrix Inverses For every non-zero real number a , there is a unique real number b for which ab=1 and ba=1 . The number b is called the multiplicative inverse of a and is denoted a1 . Dividing a number c by a is the same as multiplying c by the inverse of a . This means that division of numbers can be performed once we know how to multiply and how to compute the inverse of a non-zero number. Addition, subtraction and multiplication of matrices have been defined previously. This leads to the following natural question: is it possible to perform division using matrices? The answer is: sometimes, but not always. By analogy with what we know about numbers, we can see that we can define division of matrices if we know how to perform multiplication and if we have a notion of inverse under matrix multiplication. It turns out that this concept is only applicable to square matrices and not all of them have a multiplicative inverse. The video Invertible matrices 1 provides an introduction to the notion of inverse of a matrix. Definition: Let A be an nn matrix. An inverse of A is an nn matrix