Last Two Digits?

Notice that:

$11^2 \mod 100 =21$ ,

$11^3 \mod 100 =31$ ,

$11^4\mod 100=41$

$\dots \text { etc }$

$\implies 11^{2018} = 11^{2010+8} \mod 100 = (01)(81)= 81 \mod 100 \implies \text { the last two digits are 81. }$