The last two digits of the numbers $3^{400}$ are $01$

$\begin{array}{1 1}(A)\;\text{True}\\(B)\;\text{False}\end{array}$

$3^{400}=(3^4)^{100}$
$\qquad=(81)^{100}$
$\qquad =01$
Hence the given statement is True.