Expanding brackets with matrices is like expanding ordinary brackets, with the exception that the order of multiplication matters.
In ordinary algebra,andrepresent numbers.
In matrix algebra, ifandrepresent matrices, it is not in general the case thatFor example, ifandthen
This means that we cannot collectasorand we must be careful to preserve the order of multiplication.
Example. Ifandare matrices, expand and simplify
Simplification is possible ifsinceand