@ecterrab: Thanks four your extensive explanation. I completely agree with you when you write "As a physicist, I thought this behaviour was undesired, prone to mistakes."; as a physicist, too, I thought the very same thing. But as long as A^2 = A . A, consistently, for any square Array, I can easily live with the difference in behaviour between ^ and `.` when applied to Arrays and Matrices, respectively. I will just have to remember that it is defined that way.
PS: Using Maple 2017, can I install version 240 or later of the Physics package? I cannot, can I? If not, it is not that big a deal, for in view of the fact that I never really use elementwise multiplication of Arrays in my work, I will just have to remember to convert 2D Arrays to Matrices before multiplying them or raising them to some powers. I can live with that.