Answer
$P=\begin{bmatrix}
.1 & .8 & .1 \\
.9 & 0 & .1 \\
.5 & 0 & .5 \\
\end{bmatrix}$
Work Step by Step
Write the $ij$th entry of $P$ as the probability of transition from the state $i$ to $j$:
$1→1$: $.1$
$1→2$: $.8$
$1→3$: $.1$
$2→1$: $.9$
$2→2$: $0$
$2→3$: $.1$
$3→1$: $.5$
$3→2$: $0$
$3→3$: $.5$
So:
$P=\begin{bmatrix}
.1 & .8 & .1 \\
.9 & 0 & .1 \\
.5 & 0 & .5 \\
\end{bmatrix}$