# Becoming Number 1

How many ordered pairs of integers $$(a,b)$$ are there, subject to $$0 \leq a \leq 9$$ and $$0 \leq b \leq 9,$$ such that the units digit of $$a \times b$$ is 1?

Details and assumptions

For an ordered pair of integers $$(a,b)$$, the order of the integers matter. The ordered pair $$(1, 2)$$ is different from the ordered pair $$(2,1)$$.

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