<s>[INST] Find det(A) for matrix, find C and adj(A) I am asked to find the determinant of matrix A by using cofactors method. I understand how to do that portion, but then it asks to also find matrix C, and adj(A). How can I go about that?
for det(A) I got -20.

$ A = \begin{bmatrix}
        1 & 3 & -3 \\
        -3 & -3 & 2 \\
        -4 & 4 & -6 \\
        \end{bmatrix}$

 [/INST] $A = \begin{bmatrix}
        1 & 3 & -3 \\
        -3 & -3 & 2 \\
        -4 & 4 & -6 \\
        \end{bmatrix}$
$\det A = 4$.
We know $A^{-1}=\frac{1}{\det A} adj (A)$, where $adj$ is adjoint of matrix $A$.
$adj(A)= \left( \begin{array}{ccc} -26 & -30 & -3 \\ 10 & -6 & 7 \\ -24 & -16 & 6 \end{array} \right)$.
$\therefore A^{-1}= \frac{1}{4}\left( \begin{array}{ccc} -26 & -30 & -3 \\ 10 & -6 & 7 \\ -24 & -16 & 6 \end{array} \right)$
$A^{-1}= \left( \begin{array}{ccc} -26/4 & -30/4 & -3/4 \\ 10/4 & -6/4 & 7/4 \\ -24/4 & -16/4 & 6/4 \end{array} \right)$
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