Matriz Inversa 2×2

This calculator finds the inverse of a 2×2 matrix. The inverse of a matrix M, denoted M⁻¹, is a matrix that when multiplied by M yields the identity matrix. For 2×2 matrices, the formula is M⁻¹ = (1/det)·[[d,-b],[-c,a]], where det = a*d - b*c. The determinant must be nonzero for the inverse to exist.

The calculation is done in two steps: first, compute the determinant (det = a*d - b*c). If det = 0, the matrix is singular and has no inverse. Otherwise, swap the elements on the main diagonal (a and d), change the signs of the secondary diagonal (b and c), and divide each element by the determinant.

Use this calculator when you need to solve 2×2 systems of linear equations, find inverse transformation matrices, or in geometry and physics problems involving rotations or reflections. It is useful for students of linear algebra, engineering, and computer graphics.

Caution: check that the determinant is not zero. If it is, the matrix has no inverse. Also, remember the order of elements in the formula: a goes to position d, and b becomes -b. Common mistakes include incorrect sign changes or forgetting to divide by the determinant.