A 2×3 matrix has 2 rows and 3 columns:
[______]
Each blank position can be filled with either 0 or 1.
Total number of entries in the matrix:
2×3=6 entries
For each entry, there are exactly 2 choices: either 0 or 1.
Since each of the 6 entries has 2 independent choices:
Total number of different matrices =2×2×2×2×2×2
=26
=64
For any matrix of order m×n with each entry having k choices:
Total matrices =km×n
In this case: 22×3=26=64
Therefore, the answer is 64.