Answer
Not regular.
Work Step by Step
$A=\begin{bmatrix}
1 &0.5 \\
0 & 0.5
\end{bmatrix}$
We can see that $A$ is an upper triangular matrix and we know that any power of an upper triangular matrix is also an upper triangular matrix.
Thus no power of $A$ has only positive entries, so it cannot be regular.