linear algebra - connection between determinants

Suppose A is an nxn matrix with real entries and R is its row reduced echelon form. Using information on elementary matrices, explain the connection between det(A) and det(R). Note: you may use the fact that if M,N are two square matrices of the same size then det(MN)= det(M)det(N).

The only thing that is coming to my mind is that the A*R=A^-1, but that doesn't have anything to do with the determinant. Or the sum of the diagonal within the row reduced form is the determinant of A and if any elementary operations happens within A it is also done in R which would change the sum of the diagonal. Can someone point me in the right direction

Answer

Just use the fact that when you row reduce a matrix $A$ you can write $R = E_k E_{k-1} \cdots E_{2}E_{1}A$ where the $E_i$ are the elementary matrices. Then you have;

$$Det(R) = Det(E_k) \cdots Det(E_1) \cdot Det(A)$$