Which one of the following statements is FALSE?
1
The product of two 2 × 2 real matrices of rank 2 is of rank 2.
2
The product of two 3 × 3 real matrices of rank 2 is of rank at most 2.
3
The product of two 3 × 3 real matrices of rank 2 is of rank at least 2.
4
The product of two 2 × 2 real matrices of rank 1 can be the zero matrix.