Why is ozone a greenhouse gas if it absorb UV radiation?
Ozone is indeed a greenhouse gas. But not due to its capacity to absorb/scatter UV radiation, but instead due to its capacity to absorb infrared radiation. In contrast with other greenhouse gases (Like $CO_2$ or Methane), the spectral absorption bands of Ozone are not confined to the infrared part of the spectrum, there are ozone absorption bands also the UV too.
However, if ozone were capable to absorb only UV radiation, it would NOT be a greenhouse gas. Because the Earth's surface do not emit UV radiation.

Therefore, the greenhouse gas properties of Ozone do not come from its ultraviolet absorption bands, but instead from its infrared absorption bands, that you can see in the following infrared spectrum obtained from NIST: