Simple question about the branch number of the matrix what is the branch number of the binary identity matrix?

For example, $ I $ is 4x4 binary identity matrix, 

\begin{pmatrix}
1 &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; 1 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 1 &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 1
\end{pmatrix}

Here, the branch number is $min_x ( wt(x)+wt(Ix))=2 $. 
Is that correct?
Yes. This a degenerate matrix that provides no mixing and has minimal branch number.