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Thread: Help with determinant calculation

  1. #1
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    Help with determinant calculation

    I've got this problem:
    Let A be a 3x3 matrix. The determinant of A is 1/2 and det[(3A^2+3A+3I)(2A-2I)] =432
    Then det[A^-1(A^3-I)^3 A^-1] is : A)32 B)2 C)4*72^3 D)4*7^3 E)-7/2?

    I know the rules for determinants, for this problem is far more complex, I don't even know if I is the inverse of A or just another random matrix.

    How do you solve this?
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  2. #2
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    Re: Help with determinant calculation

    "I don't even know if I is the inverse of A or just another random matrix."

    Seriously? Obviously I is NOT "the inverse of A" because that is already represented as A^-1. I is the standard notation for the identity matrix.
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  3. #3
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    Re: Help with determinant calculation

    Quote Originally Posted by HallsofIvy View Post
    "I don't even know if I is the inverse of A or just another random matrix."

    Seriously? Obviously I is NOT "the inverse of A" because that is already represented as A^-1. I is the standard notation for the identity matrix.
    I mean the identity matrix, I was thinking about other thing
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  4. #4
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    Re: Help with determinant calculation

    Quote Originally Posted by ggaston View Post
    I've got this problem:
    Let A be a 3x3 matrix. The determinant of A is 1/2 and det[(3A^2+3A+3I)(2A-2I)] =432
    Then det[A^-1(A^3-I)^3 A^-1] is : A)32 B)2 C)4*72^3 D)4*7^3 E)-7/2?

    I know the rules for determinants, for this problem is far more complex, I don't even know if I is the inverse of A or just another random matrix.

    How do you solve this?
    Expand out your expression and then apply the properties of determinants...
    Thanks from topsquark
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