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## Homework Statement

Show that if the det(A)=1

then adj(adj(A))=A

Given Goal

det(A)=1 adj(adj(A))=A

Using the following formula A

^{-1}=adj(A)/det(A)

if det(A)=1 then A

^{-1}=adj(A)

likewise A=adj(A

^{-1})/det(A

^{-1})

if det(A)=1 then det(A

^{-1})=1

Thus A=adj(A

^{-1})

A=adj(A

^{-1})=adj(A)adj=adj(adj(A))

What i'm confused about is

Not sure if this proof is correct, TA explained it rather quickly so im running on pure memory.

I'm not sure about a few things

1.Why can we assume that det(A

2. why can we use the opposite relation to the equation A=adj(A

^{-1})/det(A

^{-1})

That's where I get a bit lost on the logic.

thanks