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    If a 23x23 matrix is such that A^T = -A , Find det(A)

    Choices are -1, 1, -23, 0, 2

    Bit confused here? I thought det(A^T) = det(A) anyway, so how does the info help me?
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    For an n\times n matrix \mathbf{A},\;\det (k\mathbf{A})=k^n\det (\mathbf{A}).
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    (Original post by Lord of the Flies)
    For an n\times n matrix A,\;\det (kA)=k^n\det (A).
    I considered that, which would make my final answer -1*det(a) but that leaves the question of what is det(a) here? how does the info provided point to that value?
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    (Original post by Zilch)
    I considered that, which would make my final answer -1*det(a) but that leaves the question of what is det(a) here? how does the info provided point to that value?
    Well, coupled with \det (\mathbf{A}^{\mathrm{T}})=\det (\mathbf{A}) we have \det (\mathbf{A})=-\det (\mathbf{A})

    What is the only number that can satisfy this?
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    (Original post by Lord of the Flies)
    Well, coupled with \det (\mathbf{A}^{\mathrm{T}})=\det (\mathbf{A}) we have \det (\mathbf{A})=-\det (\mathbf{A})

    What is the only number that can satisfy this?
    Thanks. Got it!
 
 
 
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