Category:Definitions/Inverse Matrices

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This category contains definitions related to Inverse Matrices.
Related results can be found in Category:Inverse Matrices.

Let $n \in \Z_{>0}$ be a (strictly) positive integer.

Let $\mathbf A$ be a square matrix of order $n$.

Let there exist a square matrix $\mathbf B$ of order $n$ such that:

$\mathbf A \mathbf B = \mathbf I_n = \mathbf B \mathbf A$

where $\mathbf I_n$ denotes the unit matrix of order $n$.

Then $\mathbf B$ is called the inverse of $\mathbf A$ and is usually denoted $\mathbf A^{-1}$.