1. Let A and B be unequal diagonal matrices of the same dimension. (A diagonal matrix is a square matrix in which each entry not on the main diagonal is zero.) Determine the products AB for several pairs of such matrices. Make a conjecture about a rule that can be used to calculate AB without using row-by-column multiplication.
2. Let i = ˆš-a and let

(a) Find A2, A3, and A4. Identify any similarities with i2, i3, and i4.
(b) Find and identify B2.

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and B =