Is there an explicit formula for the inverse of matrix ?
$$A\_{i,j}=a\_ib\_j$$

What is this kind of matrix called?

EDIT: It turns out that $\det A=0$ because all the columns are propertional to each other so $A$ has no inverse.

EDIT: This problem is related to another question [approximate a function by linear combination of its asympototics with fractional argument](https://math.stackexchange.com/questions/820564/approximate-a-function-by-linear-combination-of-its-asympototics-with-fractional).