Given that your conclusion is contradictory, it cannot be true in classical logic, but that doesn't necessarily mean that any argument that has it as its conlusion is invalid. It is possible for an argument to have inconsistent premises. So, for example, the following argument is valid:
- The sky is blue.
- It is not the case that the sky is blue.
- Therefore, the sky is blue and it is not the case that the sky is blue.
This is valid syntactically because 3 follows from 1 and 2 by rule of conjunction, and it is valid semantically because every model of the premises is also a model of the conclusion (because there are none of either).
The important thing to remember about validity in logic is that it is not an evaluative term meaning that an argument is good or strong or convincing. When assessing an argument it is important to ask whether it is sound (the premises are true) and whether it is cogent (the premises support the conclusion).