<Dd> N 2 = (0 0 2 7 0 0 0 3 0 0 0 0 0 0 0 0); N 3 = (0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0); N 4 = (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0). (\ displaystyle N ^ (2) = (\ begin (bmatrix) 0&0&2&7 \ \ 0&0&0&3 \ \ 0&0&0&0 \ \ 0&0&0&0 \ end (bmatrix)); \ N ^ (3) = (\ begin (bmatrix) 0&0&0&6 \ \ 0&0&0&0 \ \ 0&0&0&0 \ \ 0&0&0&0 \ end (bmatrix)); \ N ^ (4) = (\ begin (bmatrix) 0&0&0&0 \ \ 0&0&0&0 \ \ 0&0&0&0 \ \ 0&0&0&0 \ end (bmatrix)).) </Dd> <P> Though the examples above have a large number of zero entries, a typical nilpotent matrix does not . For example, the matrix </P> <Dl> <Dd> N = (5 − 3 2 15 − 9 6 10 − 6 4) (\ displaystyle N = (\ begin (bmatrix) 5& - 3&2 \ \ 15& - 9&6 \ \ 10& - 6&4 \ end (bmatrix))) </Dd> </Dl> <Dd> N = (5 − 3 2 15 − 9 6 10 − 6 4) (\ displaystyle N = (\ begin (bmatrix) 5& - 3&2 \ \ 15& - 9&6 \ \ 10& - 6&4 \ end (bmatrix))) </Dd>

Give an example of two non-zero matrices a and b such that ab is defined and equals a zero matrix