Used in test gear to detect spurious mixing products
Used in a transmitter to perform frequency multiplication
Used in an FM receiver to filter out unwanted sidebands
Used in a single sideband receiver to extract the modulated signal✓Bonne réponse
Explication
An SSB signal has had its carrier removed, so a product detector multiplies the incoming signal by a locally generated carrier and the difference product restores the original audio. Without that reinserted carrier the sideband cannot be demodulated intelligibly.