What is Inverse?

The inverse of a nonzero number $x$ is the number which multiplied by $x$ gives $1$. The inverse of $\frac ab$ is $\frac ba$, since $\frac ab \times \frac ba = \frac{ab}{ab} = 1$; the inverse of an integer $n$ is $\frac1n$.

A square matrix $A$ of size $n$ is invertible if there is a matrix $B$ with $AB = BA = I_n$; $B$ is then unique, written $A^{-1}$.