Answer: In 1418 assume the entries of all matrices are real numbers

Chapter 10, Problem 17

(choose chapter or problem)

Use mathematical induction and the result of exercise 16 to prove that if A is any \(m \times m\) matrix, then \(\mathbf{A}^{n} \mathbf{A}=\mathbf{A} \mathbf{A}^{n}\) for all integers \(n \geq 1\).

Text Transcription:

m times m

A^nA = AA^n

n geq 1

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