properties of determinants Watch

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madhapper
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#1
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#1
Let σ = (124)(35) ∈ S_5

what is σ^(-1)?

how do i find this out?
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RichE
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(Original post by madhapper)
Let σ = (124)(35) ∈ S_5

what is σ^(-1)?

how do i find this out?
what has this to do with determinants?

The answer is (142)(35)
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madhapper
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i dno but my notes say it has something to do with the det(A^T) = det(A)

how do you get (142)(35) though?
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RichE
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(Original post by madhapper)
i dno but my notes say it has something to do with the det(A^T) = det(A)

how do you get (142)(35) though?
invert each cycle separately and note

(a1 a2 ... ak)^(-1) = (ak .... a1)

and I don't see how this specific example has anything to do with proving

det(A^T) = detA

for general nxn matrices - it just takes 2-3 lines
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