# 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 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}

Here, the branch number is $min_x ( wt(x)+wt(Ix))=2$. Is that correct?