Let A and B be real matrices such that A=[α00β] and B=[0δγ0] Now, AB=[0βδαγ0] and BA=[0δαγβ0] Statement-1: AB−BA=[0δ(β−α)γ(α−β0])∣AB−BA∣=(α−β2⟩δ=0 ∴AB−BA is always an invertible matrix. Hence, statement −1 is true. But AB−BA can be identity matrix if γ=−δ or δ=−γ So, statement −2 is false.