# Another fascinating number chain!!

Take any two digit number none of whose digit is $0$. Now add the product of the digits in that number. if number becomes three digit number take last two digits. you will find a chain of numbers or a multiple of 10 after repeating this process: $02$, $04$, $08$, $16$, $22$, $26$, $38$, $62$, $74$, $102$, $04$......... Can anyone help me to prove this?