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Thread: Invertable Matrices

  1. #1
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    Invertable Matrices

    This is a post from alexdudek.

    Quote Originally Posted by alexdudek View Post
    Suppose A, B, and C are invertible 4x4 dimensional matrices with the properties that det(A)=3, det(B)=5, and det(C)=2. Calculate the determinant of:

    (3A^(-1)BCC^(T)A^(3))

    I understand matrices and determinants but I can't figure out how to start this question...Could someone help? Once I know how to set it up I think I'd be able to solve it.
    Thank you so much.
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    -Dan
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    Re: Invertable Matrices

    Here are three properties, supposing that A^(-1) is the inverse of A, and C^T is the transpose of C

    1) The determinant of a matrix product is equal to the product of the determinants. det(A1A2An)=det(A1)det(A2)det(An)
    2) det(A^(-1)) = 1/det(A)
    3) det(C^T) = det(C)

    EDIT://
    also det(cA) = c det(A) for a number c.
    Last edited by MacstersUndead; Sep 18th 2018 at 07:37 PM.
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    Re: Invertable Matrices

    Quote Originally Posted by MacstersUndead View Post
    EDIT://
    also det(cA) = c det(A) for a number c.
    Actually, $\displaystyle \det(cA) = c^n \det(A)$ for an $\displaystyle n\times n$ matrix $\displaystyle A$.

    - Hollywood
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    Re: Invertable Matrices

    You're right. Thank you for the correction.
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