Question

How to solve this?We have `M_2(ZZ_3)`second order matrix set with elements of `ZZ_3`.Determine the number of elements of the set`M_2(ZZ_3)`.

Answer 1

`81`

Explanation:

Each element of `M_2(ZZ_3)` has `2*2=4` entries taken from `ZZ_3 = { 0, 1, 2 }`.

There is no restriction on combinations of entries, so there are a total of:

`3^4 = 81`

matrices in `M_2(ZZ_3)`.