Inverse

Suppose $A$ and $B$ are square matrices of the same order. If $AB = BA = I$ then $B$ is called the inverse of $A$ and is denoted by $A^{−1}$.

$$A^{-1}=\frac{\text{adj}\,A}{\lvert{A}\rvert}$$

Singular or Non-singular

A square matrix is singular iff $\lvert{A}\rvert=0$. Otherwise its non-singular or invertible. $$

Properties of Inverse

• $(AB)^{-1}=B^{-1}A^{-1}$
• $(A^T)^{-1}=(A^{-1})^{T}$