Answer
false
Work Step by Step
We know that the determinant of a matrix \[
\left[\begin{array}{rr}
a & b \\
c &d \\
\end{array} \right]
\]
is $D=ad-bc$.
Hence for the matrix a matrix \[
\left[\begin{array}{rr}
1 & 1 \\
2 &1 \\
\end{array} \right]
\]
$D=1\cdot1-1\cdot2=1-2=-1$ whereas all the entries are positive. Thus the statement is false.