0-1 matrices are often-used in the design of diffusion structures in block ciphers. This paper first proves that the branch number of matrix over GF(2ⁿ) does not change while it is redefined over the extension field GF(2^mn). By this result, the study reinforces the proof given by Choy et al., which is about the upper bound of branch number of binary matrices over GF(2ⁿ). This paper constructs a kind of invertible binary matrices with size 8 and largest branch number, proposes a kind of matrices with equal differential branch number and linear branch number, and also includes lots of matrices and involution matrices with order 16 and optimal branch number with this structure are searched out.