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 \((2,1) \).