Question
Is it true that under certain conditions. Mg can reduce Al2O3 and Al can reduce MgO? What are those conditions?
Solution
Yes, below 1350°C Mg can reduce Al2O3 and above 1350°C. Al can reduce MgO. This can be inferred from ΔG° Vs T plots.

Fig. Gibbs energy (ΔG°) V T plots for formation of some oxides.

Fig. Gibbs energy (ΔG°) V T plots for formation of some oxides.