Solution

By definition of minors and cofactors, we have Minor of \(a_{11}\) is \(M_{11} = |\begin{smallmatrix} a_{22} & a_{23} \\ a_{32} & a_{33} \end{smallmatrix}| = a_{22}a_{33} - a_{23}a_{32}\) Cofactor of \(a_{11}\) is \(A_{11} = (-1)^{1+1} M_{11} = a_{22}a_{33} - a_{23}a_{32}\) Minor of \(a_{21}\) is \(M_{21} = |\begin{smallmatrix} a_{12} & a_{13} \\ a_{32} & a_{33} \end{smallmatrix}| = a_{12}a_{33} - a_{13}a_{32}\) Cofactor of \(a_{21}\) is \(A_{21} = (-1)^{2+1} M_{21} = -(a_{12}a_{33} - a_{13}a_{32}) = -a_{12}a_{33} + a_{13}a_{32}\)