Disclaimer: I’ve never done basketweave before. But…I would imagine that you would want to do more than a two-by-two square. I would maybe try a 4-by-4, so knit 4, purl 4, for a row. Remember that for the next row, when you’re working back in the other direction, you want to switch the order and start with purl 4, then knit 4. Repeat for 4 rows then switch the pattern, reversing when you purl and when you knit. Make sure that if you purled going one direction, then you should knit those same stitches when you’re heading back in the other direction, and vice versa.
In sum: I think 2×2 would be a little too small, and would end up looking like a weird ribbed pattern instead of basket weave. Something bigger will end up looking more like a standard basket weave pattern. But there’s only one way to know for sure! Try and see!
Feel free to respond if this doesnt make sense to you, i’m writing in a hurry and I may not have made myself clear.