The minor of A are 3,-3,-3,14,-1,-6,-78,0,42 and cofactors of A are 3,-3,-3,14,-1,-6,-78,0,42.
To find the minors and cofactors of matrix A, we need to first understand what minors and cofactors are.
The minor of an element in a matrix is the determinant of the submatrix formed by deleting the row and column containing that element.
The cofactor of an element is the minor multiplied by (-1) raised to the power of the sum of the row and column indices of that element.
To find the minors and cofactors of A, we calculate the minors and cofactors of each element in A.
The minors are:
Minor of A[1][1] = determinant of [[9, 6], [-2, -3]] = (9*(-3) - 6*(-2)) = 3
Minor of A[1][2] = determinant of [[3, 6], [-1, -3]] = (3*(-3) - 6*(-1)) = -3
Minor of A[1][3] = determinant of [[3, 9], [-1, -2]] = (3*(-2) - 9*(-1)) = -3
Minor of A[2][1] = determinant of [[-8, 5], [-2, -3]] = (-8*(-3) - 5*(-2)) = 14
Minor of A[2][2] = determinant of [[2, 5], [-1, -3]] = (2*(-3) - 5*(-1)) = -1
Minor of A[2][3] = determinant of [[2, -8], [-1, -2]] = (2*(-2) - (-8)*(-1)) = -6
Minor of A[3][1] = determinant of [[-8, 5], [9, 6]] = (-8*6 - 5*9) = -78
Minor of A[3][2] = determinant of [[2, 5], [3, 6]] = (2*6 - 5*3) = 0
Minor of A[3][3] = determinant of [[2, -8], [3, 9]] = (2*9 - (-8)*3) = 42
The cofactors are obtained by multiplying each minor by (-1) raised to the power of the sum of the row and column indices.
The cofactors of A are:
Cofactor of A[1][1] = 3
Cofactor of A[1][2] = -3
Cofactor of A[1][3] = 3
Cofactor of A[2][1] = 14
Cofactor of A[2][2] = -1
Cofactor of A[2][3] = -6
Cofactor of A[3][1] = -78
Cofactor of A[3][2] = 0
Cofactor of A[3][3] = 42
The probable question may be:
Find all the minors and cofactors of A = \left[\begin{array}{ccc}2&-8&5\\3&9&6\\-1&-2&-3\end{array}\right]