Cofactor matrix of $$$\left[\begin{array}{cc}t & - t\\0 & t\end{array}\right]$$$
Your Input
Find the cofactor matrix of $$$\left[\begin{array}{cc}t & - t\\0 & t\end{array}\right]$$$.
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:
$$$C_{11} = \left(-1\right)^{1 + 1} \left|\begin{array}{c}t\end{array}\right| = t$$$ (for steps, see determinant calculator).
$$$C_{12} = \left(-1\right)^{1 + 2} \left|\begin{array}{c}0\end{array}\right| = 0$$$ (for steps, see determinant calculator).
$$$C_{21} = \left(-1\right)^{2 + 1} \left|\begin{array}{c}- t\end{array}\right| = t$$$ (for steps, see determinant calculator).
$$$C_{22} = \left(-1\right)^{2 + 2} \left|\begin{array}{c}t\end{array}\right| = t$$$ (for steps, see determinant calculator).
Thus, the cofactor matrix is $$$\left[\begin{array}{cc}t & 0\\t & t\end{array}\right]$$$.
Answer
The cofactor matrix is $$$\left[\begin{array}{cc}t & 0\\t & t\end{array}\right]$$$A.