Final answer:
The question requires calculating the inverse of a 2x2 matrix multiplied by the scalar 1 over the determinant. However, the provided options merely suggest dividing matrix elements by a scalar, which by itself would not produce an inverse matrix. Therefore, none of the options given are correct for finding the inverse of a matrix.
Step-by-step explanation:
The question pertains to finding the inverse of a 2x2 matrix multiplied by the scalar 1 over the determinant of the matrix. The given matrix A^(-1) = a11 a12 a21 a22 has elements a11, a12, a21, and a22. When we multiply by the scalar (1/det(A)), where det(A) represents the determinant of matrix A, each element of the inverse matrix A^(-1) is scaled by that amount.
To obtain The inverse of a matrix, you need to perform certain operations. However, the options given do not represent the full process of finding the inverse of a matrix due to the lack of a transpose of the cofactor, among other missing elements. Instead, the provided options suggest merely dividing elements of a matrix by a scalar, which alone would not yield an inverse matrix.
Therefore, none of the given options, B, C, or D are correct expressions for the inverse of a matrix when multiplied by the scalar 1 over the determinant. Typically, to find the inverse of a 2x2 matrix, you would swap the elements a11 and a22, change the signs of a12 and a21, and then multiply each by 1 over the determinant.