The total number of possible matrices of order 3 × 3 with each entry 2 or 0 is

We know that a matrix 3× 3 contains 9 elements. Given that each entry of this 3× 3 matrix is either 0 or 2.

Thus, by simple counting principle, we can calculate the total number of possible matrices as:

Total number of possible matrices = Total number of ways in which 9 elements can take possible values

= 2⁹
= 512