If B is the inverse of n × n matrix A, then Definition 1.10 guarantees that AB = BA = In ....

If B is the inverse of n × n matrix A, then Definition 1.10 guarantees that AB = BA = In .The unstated assumption is that exact arithmetic is used. If computer arithmetic is used to compute AB, then AB need not equal In and, in fact, BA need not equal AB. However, both AB and BA should be close to In. In your software, use the inverse command (see Exercise 63) and form the products AB and BA for each of the following matrices:

(a) A =

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(b)  A

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(c)  A