Let Mn (ℝ) be the ring of n × n matrices over ℝ. Which of the following are true for every n ≥ 2 ?
1
there exist matrices A, B ∈ Mn (ℝ) such that AB - BA = In, where In denotes the identity n × n matrix.
2
if A, B ∈ Mn, (ℝ) and AB = BA, then A is diagonalisable over ℝ if and only if B is diagonalizable over ℝ
3
if A, B ∈ Mn, (ℝ), then AB and BA have same minimal polynomial
4
if A, B ∈ Mn (ℝ), then AB and BA have the same eigenvalues in ℝ