Alright,,, i had a linear algebra exam and i messed up real good in it,,, its one of the worst exams i've ever had,,, anyways ,,,since the whole class messed up in it ,,the professor gave us a Problem to Solve so we can fix our marks with ,,, 5 marks for anyone who solves it ,,, i have been thinking about it through the week,,,and couldn't solve it,,,,then i tried to go to the libary,,,search some books,,,,but still,,,,i've got nothing!!

here is the Problem:
If A is a 2x3 matrix ,and B is a 3x2 matrix, find det[AB] without multiplying A and B, then try to state the general rule if A was mXn and B was nXp?

wtf?!?! how am i suppose to solve it?!?!
Please help ,,,,,!!! I'll be incredibly grateful!
PS: we didn't start the chapters talking about Real Vector Spaces and all that stuff,,,,so keep it in simple determinants and matrices theorems,