Value of the determinant of a matrix A of order 3 3 is 7 . Then the value of the determinant formed by the cofactors of matrix A is

Step-by-step solution

Let A be a square matrix of order n n . The matrix formed by the cofactors of A is denoted by C . The property relating the determinant of the cofactor matrix to the determinant of the original matrix is given by |C| = |A|^ n-1 . In this problem, the order of matrix A is n = 3 and the determinant of A is |A| = 7 . Substituting these values into the formula: |C| = 7³⁻¹ = 7^2 = 49 . Answer: 49