Matrix division does not denote a single operation having all the properties of scalar division. If 
is an invertible square matrix, one common convention
defines right division and left division respectively by
 |
These expressions generally differ because matrix multiplication is not commutative. More broadly,
solving 
or 
is preferable to explicitly forming an inverse. A rectangular system has a rectangular
matrix of coefficients, while a singular system
has a singular matrix and no ordinary inverse.
Such linear systems may instead be treated
using a pseudoinverse or least
squares solution.
