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Let A E Mnxn(F) and B = aA, with a E F. Prove by induction that det(B) = a" det(A), for all positive integer n.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.4: Prime Factors And Greatest Common Divisor

Problem 32E: Use the second principle of Finite Induction to prove that every positive integer n can be expressed...

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Let A E Mnxn(F) and B = aA, with a E F. Prove by induction that det(B) = a" det(A), for
all positive integer n.

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