Final answer:
To find the inverse of a 2x2 matrix, use the formula A⁻¹ = 1/det(A) * adj(A). Calculate the determinant and adjugate matrix, then multiply by the reciprocal of the determinant.
Step-by-step explanation:
To find the inverse of a 2x2 matrix, we can use the formula:
A⁻¹ = 1/det(A) * adj(A)
Where det(A) is the determinant of matrix A and adj(A) is the adjugate matrix of A. For the given matrix [-7 4] [8 -5], we can calculate these values as follows:
det(A) = (-7 * -5) - (4 * 8) = 35 - 32 = 3
adj(A) = [-5 -4] [8 -7]
Therefore, the inverse of the matrix is:
A⁻¹ = 1/3 * [-5 -4] [8 -7]