Determine the cofactor of $a_{32}$ in the matrix. \[ A=\left[\begin{array}{ccc} 8 & -1 & 8 \\ 0 & 2 & 1 \\ 7 & 1 & -7 \end{array}\right] \]

Step 1 ：We are given the matrix A = \(\left[\begin{array}{ccc} 8 & -1 & 8 \\ 0 & 2 & 1 \\ 7 & 1 & -7 \end{array}\right]\)

Step 2 ：We want to find the cofactor of the element at the 3rd row and 2nd column, denoted as \(a_{32}\).

Step 3 ：To find the cofactor, we first remove the 3rd row and 2nd column from the matrix. This gives us a new 2x2 matrix: \(\left[\begin{array}{cc} 8 & 8 \\ 0 & 1 \end{array}\right]\)

Step 4 ：We then calculate the determinant of this 2x2 matrix. The determinant is calculated as \((8*1) - (8*0) = 8\)

Step 5 ：Finally, we multiply this determinant by \((-1)^{3+2}\), which is -1. So, the cofactor of \(a_{32}\) is \(-1 * 8 = -8\)

Step 6 ：\(\boxed{-8}\) is the cofactor of \(a_{32}\) in the matrix.