Find the cofactor matrix of the following 3x3 matrix: \[A = \begin{bmatrix} 1 & 2 & 3 \\ 0 & 4 & 5 \\ 1 & 0 & 6 \end{bmatrix}\]

Step 1 ：First, we calculate the determinant of 2x2 sub-matrices for each element of the matrix A. We start with the element at the first row and first column (i.e., 1). The 2x2 sub-matrix for this element (obtained by removing the first row and the first column) is: \[\begin{bmatrix} 4 & 5 \\ 0 & 6 \end{bmatrix}\] The determinant of this sub-matrix is \((4 \times 6) - (5 \times 0) = 24\). The cofactor of the element at the first row and first column is \((-1)^{1+1} \times 24 = 24\).

Step 2 ：Similarly, we find the cofactors of all other elements of the matrix A: \[C = \begin{bmatrix} 24 & -5 & 20 \\ -30 & 6 & -5 \\ -20 & -15 & 4 \end{bmatrix}\]

Step 3 ：Finally, we apply the transformation \((-1)^{i+j}\) to each element in the cofactor matrix C to get the cofactor matrix of A: \[Cof(A) = \begin{bmatrix} 24 & 5 & -20 \\ 30 & 6 & 5 \\ -20 & 15 & 4 \end{bmatrix}\]