The value of the determinant of a matrix A of order 3 is 3. If C is the matrix of cofactors of the matrix A, then what is the value of determinant of C^2?

Explanation

The cofactor matrix C is adj(A)^T, so its determinant is det(C) = det(adj(A)) = (det(A))^{n-1} = 3^2 = 9. We need det(C^2) = (det(C))^2 = 9^2 = 81.

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