A matrix substrate which realizes high operation speed and high reliability and which is capable of obtaining a high-quality image while the number of connection terminals is limited is provided. The matrix substrate includes pixels arranged in a matrix, N driving lines arranged in a row direction, P connection terminals where P is less than N, a demultiplexer which is disposed between the connection terminals and the driving lines and which includes first polycrystalline semiconductor TFTs and first connection terminals. The demultiplexer further includes second polycrystalline semiconductor TFTs and the second control lines used to maintain the driving lines to have non-selection voltages which bring the pixels to non-selection states between one of the connection terminals and two or more of the driving lines.