Aggregating data by date between tabs stackoverflow

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I have three tabs:

1. Transactions
2. Payees
3. Categories

This is what my Transactions tab looks like:

+--------------+-------------+-----------+
|         Date |       Payee |    Amount |
+--------------+-------------+-----------+
|   29/03/2020 |   Company 1 |   $100.00 |
+----------------------------------------+
|   27/02/2020 |   Company 1 |   $220.00 |
+----------------------------------------+
|   12/02/2020 |   Company 2 |   $350.00 |
+----------------------------------------+
|   05/01/2020 |   Company 2 |    $50.00 |
+----------------------------------------+
|   28/03/2020 |   Company 1 |   $125.00 |
+--------------+-------------+-----------+

This is what my Payees tab looks like:

+-------------+------------+
|       Payee |   Category |
+-------------+------------+
|   Company 1 |        Gas |
+--------------------------+
|   Company 2 |  Groceries |
+-------------+------------+

As you can see, each company is associated with a category.

This is what my Categories tab looks like:

+-------------+-----------+-----------+-----------+
|    Category |   03/2020 |   02/2020 |   01/2020 |
+-------------+-----------+-----------+-----------+
|         Gas |           |           |           |
+-------------------------------------------------+
|   Groceries |           |           |           |
+-------------+-----------+-----------+-----------+

As you can see in my Categories tab, there are empty columns for the months. What I want to do is fill these columns by aggregating total amounts by category.

In the end, the Categories tab should look like this:

+-------------+-----------+-----------+-----------+
|    Category |   03/2020 |   02/2020 |   01/2020 |
+-------------+-----------+-----------+-----------+
|         Gas |   $225.00 |   $220.00 |        $0 |
+-------------------------------------------------+
|   Groceries |        $0 |   $350.00 |    $50.00 |
+-------------+-----------+-----------+-----------+

How would I go about combining this data?

And additionally, is it possible to create a new column in the Categories tab if a new transaction is added to the Transactions tab for a new month, e.g. 04/2020?

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