The most known solutions to the Quantum Yang-Baxter Equation are those related to the Drinfeld-Jimbo Quantum Groups. However, there exists a big family of others. To some of them one can associate quantum algebras such as "RTT" algebra and Reflection Equation algebra (modified or not). They possess some remarkable properties, one of them is the Cayley-Hamilton identity valid for certain matrices with entries from these algebras. Some applications of this identity to Noncommutative Geometry and Mathematical Physics will be presented.