Let A be a nonsingular n × n matrix. Use mathematical induction to prove that Am is nonsingular and (Am)−1 = (A−1)m for m = 1, 2, 3, . . . .

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Chapter3: Determinants
Section3.CM: Cumulative Review
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Let A be a nonsingular n × n matrix. Use mathematical
induction to prove that Am is nonsingular and
(Am)−1 = (A−1)m
for m = 1, 2, 3, . . . .

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