Solve this following

If the points $\mathrm{A}(\mathrm{a}, 0), \mathrm{B}(0, \mathrm{~b})$ and $\mathrm{C}(1,1)$ are collinear, prove that $\frac{1}{\mathrm{a}}+\frac{1}{\mathrm{~b}}=1$.