Matrix of minors of $$$\left[\begin{array}{cc}1 & 2\\3 & 4\end{array}\right]$$$

Find the matrix of minors of $$$\left[\begin{array}{cc}1 & 2\\3 & 4\end{array}\right]$$$.

The matrix of minors consists of all minors of the given matrix.

Minor $$$M_{ij}$$$ is the determinant of the submatrix formed by deleting row $$$i$$$ and column $$$j$$$ from the given matrix.

Calculate all minors:

$$$M_{11} = \left|\begin{array}{c}4\end{array}\right| = 4$$$ (for steps, see determinant calculator).

$$$M_{12} = \left|\begin{array}{c}3\end{array}\right| = 3$$$ (for steps, see determinant calculator).

$$$M_{21} = \left|\begin{array}{c}2\end{array}\right| = 2$$$ (for steps, see determinant calculator).

$$$M_{22} = \left|\begin{array}{c}1\end{array}\right| = 1$$$ (for steps, see determinant calculator).

Thus, the matrix of minors is $$$\left[\begin{array}{cc}4 & 3\\2 & 1\end{array}\right]$$$.

The matrix of minors is $$$\left[\begin{array}{cc}4 & 3\\2 & 1\end{array}\right]$$$A.