(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that it is false

If A is invertible and A^{-1}= adj A, then det A= 1

2. Relevant equations

N/A

3. The attempt at a solution

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A is invertible iff A^{-1}A = I

implies det(A^{-1}A) = det(I)

implies det(A^{-1})det(A) = 1

implies det(A) = 1 or -1--------------------------------this is wrong, just ignore this part (edited)

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AND

A^{-1}= adj(A)

which is false because

A^{-1}= [tex]\frac{1}{det(A)}[/tex] adj(A)

so, which means the premise is already false

false implies (true or false)

is a true statement

so, is it the question wrong, or i did any mistake?

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# Homework Help: Proving a Linear System

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