Can I hide all unused columns and rows in Excel by keyboard?

One way would be to use the {End}(Home} keys to jump to the last used cell and move one cell to the right.
Then hold the shift key down and {End} (Right} to select all the unused columns, then choose Format..Hide & Unhide and pick the hide columns
Now move one cell down
Then hold the shift key down and {End} (Down} to select all the unused rows, then choose Format..Hide & Unhide and pick the hide rows.