Invertible matrix

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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. This matrix has ones on its main diagonal, and 0 everywhere else. The matrix which can achieve this result is called inverse:

A \cdot A^{-1} = I

There are algorithms to calculate the inverse of a matrix, for example Gaussian elimination. The problem is that finding the inverse is relatively expensive to do for big matrices. Matrix inversion is used extensively in computer graphics.