Determine if the statement is true or false, and justify your answer. You may assume that A and B are n × n matrices. If A and B are diagonal matrices, then so is A − B. True. If i ≠ j, then Aij = Bij = 0, so (A − B)ij = 0, and A − B is diagonal. True. If i = j, then Aij = Bij = 0, so (A − B)ij = 0, and A − B is diagonal. False. If i = j, then (A − B)ij = Aij − Bij may not be zero, so A − B is not necessarily diagonal. False. If i ≠ j, then (A − B)ij = Aij − Bij may not be zero, so A − B is not necessarily diagonal. False. If i ≠ j, then Aij = −Bij, so (A − B)ij = 2Aij, and A − B is not diagonal.