Expanding brackets with matrices is like expanding ordinary brackets, with the exception that the order of multiplication matters.
In ordinary algebra,
and
represent numbers.
In matrix algebra, if
and
represent matrices, it is not in general the case that
For example, if
and
then
but
This means that we cannot collect
as
or
and we must be careful to preserve the order of multiplication.
Example. Ifandare matrices, expand and simplify
Simplification is possible if
since
and
