Tax issues for working in US, living in Canada

Hiya. I'm sort of confused about the tax related issues with working over the border. I'm going to be going to school in Canada, so I most likely will have to establish residency in Ontario. But I probably will have to work in NY state. Would I have to pay taxes in both Canada and the US?

Or, conversely, is there any way I could live in the US, without having a Canadian residence, and still go to school in Ontario?

Work permits in either aren't really an issue because I'm a Canadian citizen, and a permanent resident in the US.

Thanks for your help!

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