What is the purpose of a matrix switcher in an AV system?

The purpose of a matrix switcher in an AV system is to route multiple input sources to multiple output destinations. This device allows users to select which input signal (such as a video feed or audio source) will be directed to any output destination (like a display, projector, or speaker). This capability is particularly valuable in environments where various content sources need to be easily accessed and displayed or played through different outputs without needing to physically change cables or connections.

Matrix switchers often support a range of input and output formats, enabling seamless switching between different devices, such as Blu-ray players, computers, cameras, and more. This flexibility is crucial for managing complex AV setups in venues like conference rooms, theaters, or broadcast studios, where multiple sources need to be available for dynamic presentations or performances. Other options presented in the question, such as amplifying signals, converting formats, or storing content, do not encapsulate the primary function of directing signals in an effective and organized manner, which is the hallmark of a matrix switcher.