The trick here was to take the last digit (the units) in your answer.

1x1 = 1. because 1 is an 1 digit number

2x2= 4. 4 is an 1 digit number.

3x3 = 9. 9 is also an 1 digit number.

BUT 4X4 = 16. 16 is a 2-digit number. From the clue we have 4x4 = 6 (taking the last number)

5X5 = 25. 25 is a 2-digit number. From the clue we have 5x5 = 5 (taking the last number)

7X7 = 49. 49 is a 2-digit number. From the clue we have 7x7 = 9 (taking the last number)

So, 9x9 = 1 because 9x9 = 81 ans we take the 1. Easy as that!