Hello. I want to find the last 2 digits of 3^400 using modular arithmetic. What I have so far...

3^20 congruent to 1 (mod 25) using Euler's theorem.

3^2 congruent to 1 (mod 4) using Euler's theorem again.

I want to somehow reach 3^20 congruent to 1 (mod 100), and from there show that the last two digits are 01, but I have no clue. Can anyone help?