adding up a column based on the category from anothe column & date range of another column

I'm sorry if this has been asked and answered already. It's a specific problem I have trouble putting into words. I attached a picture for easier reference.
I want to add up the sum of all items based on matching categories (column B) and within a specific date range from Column A. For example I want all items under Supplies & Materials within January to be added together.

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