Can I claim rent and Hydro bills in Quebec when my permanent residence is in Ontario?

Rent for Tax Return in Quebec

Quebec offers the Solidarity Tax Credit (Crédit d’impôt de Solidarité) as a refundable credit for low and middle income families. There are three components to this credit:

• Housing
• QST
• If individuals are living in northern villages

An individual may qualify for all or some of these components. You must be at least 18 years old and a Canadian citizen. When claiming this credit, you can indicate your addresses where rent was paid and the total amount paid in the given tax year. The amount you are eligible for depends on your income, expenses, and location in the given year.
To see if you are eligible for the same please check : https://www.revenuquebec.ca/en/citizens/tax-credits/solidarity-tax-credit/eligibility/
To see if you are a Quebec resident check the following: 
https://www.quebec.ca/en/education/student-financial-assistance/loans-bursaries-full-time-studies/eligibility-requirements
And then you can also check the following: