Cayley algebra is the branch of the non-commutative algebras dealing with matrices. English mathematician Arthur Cayley developed it during 1840 to 1890. It is the only non-associative division algebra with real scalars. Division algebra is a type of algebra in which every nonzero element has a multiplicative inverse but where multiplication is non-commutative, that is x * y y * x.

Arthur Cayley, considered a British mathematician although he practiced law the first 14 years of his professional career, was part of the movement in the 19th century by British mathematicians to study algebras. During these studies of various sorts of mathematical objects Cayley turned his attention to matrices and assorted operations that could be performed on them. This was a time when the scope of algebra was expanded and not limited to ordinary systems of numbers alone and one of the most important developments was the formulation of non-commutative algebras...