# Invertible matrix

square matrix with non-zero determinant

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 ${\displaystyle I}$ (the matrix with ones on its main diagonal and 0 everywhere). If ${\displaystyle A}$ is such a matrix, then ${\displaystyle A}$ is called invertible and its inverse is called ${\displaystyle A^{-1}}$,[1] with:[2]

${\displaystyle A\cdot A^{-1}=A^{-1}\cdot A=I}$

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.

## References

1. "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-09-08.
2. Weisstein, Eric W. "Matrix Inverse". mathworld.wolfram.com. Retrieved 2020-09-08.