Unformatted text preview: ...”]. Can m = n ? If so, and m = n , what can you say about A ? Problem 3 Suppose that two square matrices satisfy the following identity AB =BA . Find the ﬂaw in the following argument, showing a counterexample: Taking determinants gives (det A )(det B ) =(det B )(det A ), so either A or B must have zero determinant. Thus AB =BA is only possible if A or B is singular. 1...
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 Spring '05
 CONSANI
 Linear Algebra, Algebra, Determinant, Vector Space, Invertible matrix, Det

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