# Cofactor Matrix Calculator

The calculator will find the matrix of cofactors of the given square matrix, with steps shown.

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Find the cofactor matrix of $$\left[\begin{array}{ccc}1 & 2 & 3\\4 & 5 & 6\\7 & 8 & 9\end{array}\right]$$$. ## Solution The cofactor matrix consists of all cofactors of the given matrix, which are calculated according to the formula $$C_{ij}=\left(-1\right)^{i+j}M_{ij}$$$, where $$M_{ij}$$$is the minor, i.e. the determinant of the submatrix formed by deleting row $$i$$$ and column $$j$$$from the given matrix. Calculate all cofactors: $$C_{11} = \left(-1\right)^{1 + 1} \left|\begin{array}{cc}5 & 6\\8 & 9\end{array}\right| = -3$$$ (for steps, see determinant calculator).
$$C_{12} = \left(-1\right)^{1 + 2} \left|\begin{array}{cc}4 & 6\\7 & 9\end{array}\right| = 6$$$(for steps, see determinant calculator). $$C_{13} = \left(-1\right)^{1 + 3} \left|\begin{array}{cc}4 & 5\\7 & 8\end{array}\right| = -3$$$ (for steps, see determinant calculator).
$$C_{21} = \left(-1\right)^{2 + 1} \left|\begin{array}{cc}2 & 3\\8 & 9\end{array}\right| = 6$$$(for steps, see determinant calculator). $$C_{22} = \left(-1\right)^{2 + 2} \left|\begin{array}{cc}1 & 3\\7 & 9\end{array}\right| = -12$$$ (for steps, see determinant calculator).
$$C_{23} = \left(-1\right)^{2 + 3} \left|\begin{array}{cc}1 & 2\\7 & 8\end{array}\right| = 6$$$(for steps, see determinant calculator). $$C_{31} = \left(-1\right)^{3 + 1} \left|\begin{array}{cc}2 & 3\\5 & 6\end{array}\right| = -3$$$ (for steps, see determinant calculator).
$$C_{32} = \left(-1\right)^{3 + 2} \left|\begin{array}{cc}1 & 3\\4 & 6\end{array}\right| = 6$$$(for steps, see determinant calculator). $$C_{33} = \left(-1\right)^{3 + 3} \left|\begin{array}{cc}1 & 2\\4 & 5\end{array}\right| = -3$$$ (for steps, see determinant calculator).