<p>In reality, the observations of variables is often represented as a matrix. For example, in the observation of air quality, the changes of multiple objects at different time points in each day can be viewed as a matrix. Considering the influence of each individual, this paper proposes a binary coefficient autoregressive model with fixed effects for panel matrix-valued data. Here two kinds of estimations are introduced to calculate the left and right coefficients. The first one is the generalized moment method (GMM), which can avoid the endogeneity problem caused by difference. After that, in order to select the elements with strong correlation in the matrix and make the unnecessary shrinkage to zero, the least absolute shrinkage and selection operator (LASSO)-type GMM is introduced, which can save calculation cost. The proposed GMM estimation and LASSO-type GMM estimation are consistent and asymptotically centered normal. Then Monte Carlo simulation and empirical application are carried out to show that our proposed model is an effective tool for analyzing panel matrix-valued data.</p>