How many diagonal matrices of order 3 × 3 can be formed if each element is 0 or 1?

Explanation

1. 01

   In a diagonal matrix every element off the leading diagonal must be 0, so only the 3 diagonal places are free.

2. 02

   Each has 2 choices, so there are $2^3 = 8$ such matrices (the zero matrix and $I$ among them).