Suppose that $A$ is a nonsingular matrix of size $n$ that is triangular. Then the inverse of $A$, $\inverse{A}$, is triangular of the same type. Furthermore, the diagonal entries of $\inverse{A}$ are the reciprocals of the corresponding diagonal entries of $A$. More precisely, $\matrixentry{\inverse{A}}{ii}=\matrixentry{A}{ii}^{-1}$.