Question

Why can't the product of two 2-digit numbers ever be two digits

Answer 1

let's try with the smallest one: 10*10=100
those are the digits and the bigger ones may be even bigger than 3 digits, but never lower than 2

Answer 2

Because the lowest two digit number is 10 and 10 • 10 = 100 so you are already into the three digit numbers and will only go higher.