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Any one help. Adjugate of 2X2 matrix

  1. Sep 2, 2009 #1
    I know how to find the adjugate of 3x3 matrix. from the defination.

    How to find adjugate of 2x2 matrix.

    e.g A= ( 1 3 )
    ______( 2 4 )

    adjoint .

    I know how to find adjugate and inverse. of 3 * 3 matrix

    First . I find matrix of cofactor. from the defination. (n-1)(n-1) matrix * (sign associated with the element's position).

    Second, we taking the transpose we get the adj(A)

    Then we find the det(A).

    Finally, A^-1 = 1/det(A) * adj(A)

    The inverse of A.

    [itex]AA^- = A^-A=I[/itex] and A adj(A) = det(A)I

    The inverse of [itex]A = det(A)I/ A^-[/itex]
  2. jcsd
  3. Sep 2, 2009 #2


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    Staff Emeritus
    Science Advisor

    Isn't [tex]\text{adj}\left(\begin{array}{cc}a&b\\c&d\end{array}\right)=\left(\begin{array}{cc}d&-b\\-c&a\end{array}\right)[/tex]?
  4. Sep 2, 2009 #3
    Just remember it? right?
  5. Sep 2, 2009 #4


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    Homework Helper

    yes, that is it for a 2x2 matrix, switch elements 1 and 4; change the sign of elements 2 and 3
  6. Sep 3, 2009 #5
    OK. thx. :rofl:
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