Unformatted text preview: 27. (Statement of the problem.) Proof. Since A and B are symmetric, by the definition we have AT = A, B T = B. () "=" Suppose that AB = BA. Then (AB)T = (BA)T = AT B T (By Algebraic Rule 4 for Transpose) = AB (By (*) ) By definition of symmetry, AB is symmetric. "=" Suppose that AB is symmetric. Then AB= (AB)T (By definition of symmetry) (By Algebraic Rule 4 for Transpose) = B T AT = BA (By (*) ) That is, AB = BA. 1 ...
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This note was uploaded on 04/01/2008 for the course MATH 309 taught by Professor Samiabdul during the Spring '08 term at Michigan State University.
 Spring '08
 samiabdul
 Linear Algebra, Algebra

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