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Matrix Algebra Worksheet 1 Solutions - University of California, Berkeley

Math 10B Spring 2018 Matrix Algebra Worksheet 1 Solutions (i)Write 2 2 matrices A, B, C such that AB = AC but B 6= C. Solution: First, a helpful observation. Suppose A is invertible and AB = AC. Then multiplying both sides by A 1 gives A 1(AB) = A 1(AC). Using distributivity and the fact that A 1A = I, this implies that IB = IC and therefore B = C.