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If A, B, and C are invertible matrices, the expression (AB^-1)^-1(CA^-1)^-1C2 evaluates to ____________(a) BC(b) C^-1BC(c) AB^-1(d) C^-1BI had been asked this question during an online exam.This question is from Groups topic in section Groups of Discrete Mathematics |
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Answer» CORRECT ANSWER is (a) BC The EXPLANATION: Using the properties (AB)^-1=b^-1A^-1 and (A^-1)^-1=A, we may have, (AB^-1)^-1(CA^-1)^-1C2 =(B^-1)^-1A^-1(A^-1)^-1C^-1C2 =BA^-1AC^-1C2 =BIC=BC [As, A^-1A=I]. |
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