which does not arise in ordinary algebra where the order of multiplying two
numbers together makes no difference to the answer.
Another difference occurs with inverses. In ordinary algebra inverses are easy
to calculate. If a= 7 its inverse is 1/7 because it has the property that 1/7 × 7 =
- We sometimes write this inverse as a–1 = 1/7 and we have a−1 × a = 1.
An example in matrix theory is and we can verify thatbecausewhere is called the identity matrix and is the matrix counterpart of 1
in ordinary algebra. In ordinary algebra, only 0 does not have an inverse but in
matrix algebra many matrices do not have inverses.