We denote by In the n × n identity matrix. Which one of the following statements is true?
1
If A is a real 3 × 2 matrix and B is a real 2 × 3 matrix such that BA = I2, then AB = I3.
2
Let A be the real matrix \(\left(\begin{array}{ll}3 & 3 \\ 1 & 2\end{array}\right)\). Then there is a matrix B with integer entries such that AB = I2.
3
Let A be the matrix \(\left(\begin{array}{ll}3 & 1 \\ 1 & 2\end{array}\right)\) with entries in ℤ/6ℤ. Then there is a matrix B with entries in ℤ/6ℤ such that AB = I2.
4
If A is a real non-zero 3 × 3 diagonal matrix, then there is a real matrix B such that AB = I3.