MATLAB® is a programming platform designed specifically for engineers and scientists to analyze and design systems and products that transform our world.
The heart of MATLAB is the MATLAB language, a matrix-based language allowing the most natural expression of computational mathematics.
MATLAB language is the first (and often only) programming language for many engineers and scientists because the matrix math and array orientation of the language makes it easy to learn and apply to engineering and scientific problem-solving.
MATLAB is a programming language in and of itself.
However, various parts of MATLAB and the associated development environment are written in C (the core framework), C++ (I know that the Parallel computing part is written in C++, I assume other parts are as well) and Java (most of the interfaces).