Commuting matrices

In linear algebra, two matrices formula_1 and formula_2 are said to commute if formula_3, or equivalently if their commutator formula_4 is zero. A set of matrices formula_5 is said to commute if they commute pairwise, meaning that every pair of matrices in the set commute with each other.
History.
The notion of commuting matrices was introduced by Cayley in his memoir on the theory of matrices, which also provided the first axiomatization of matrices. The first significant results proved on them was the above result of Frobenius in 1878.