The [[Inverse Property|inverse]] of a [[Quaternions|quaternion]] $q$ is defined as the [[Multiplicative Group|multiplicative]] [[Inverse Property|inverse]] $q^{-1}$, where multiplication of $q$ and $q^{-1}$ leads to the [[Scalar|scalar]] [[Identity Property|identity]] of $\H$. $\huge \begin{align} qq^{-1} &= 1 \\ q^{-1}q &= 1 \\ q^{-1} &= \frac{q^{*}}{|q|^{2}} \end{align} $ The inverse of a quaternion is relatively easy to compute compared to a [[Inverse Matrices|Matrix Inverse]] as it is just the [[Quaternion Conjugate|conjugate]] of $q$ divided by its square [[Vector Magnitude|magnitude]].