Invertible matrix

In linear algebra, there are certain matrices which have the property that when they are multiplied with another matrix, the result is the identity matrix formula_1 (the matrix with ones on its main diagonal and 0 everywhere). If formula_2 is such a matrix, then formula_2 is called invertible and its inverse is called formula_4, with:
There are algorithms for calculating the inverse of a matrix, with Gaussian elimination being a common example. The problem is that finding the inverse is relatively "expensive" to do for big matrices. Matrix inversion is used extensively in computer graphics.