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Adjoint of $$$\left[\begin{array}{cc}a & b\\c & d\end{array}\right]$$$
Your Input
Find the adjoint matrix of $$$\left[\begin{array}{cc}a & b\\c & d\end{array}\right]$$$.
Solution
The classical adjoint, adjugate, or adjunct of a square matrix is the transpose of its cofactor matrix.
The cofactor matrix is $$$\left[\begin{array}{cc}d & - c\\- b & a\end{array}\right]$$$ (for steps, see cofactor matrix calculator).
The transpose of the cofactor matrix is $$$\left[\begin{array}{cc}d & - b\\- c & a\end{array}\right]$$$ (for steps, see matrix transpose calculator).
Answer
The adjoint matrix is $$$\left[\begin{array}{cc}d & - b\\- c & a\end{array}\right]$$$A.
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