The Inverse Calculator finds the inverse of matrices. Enter a square matrix and the calculator will compute its inverse if it exists, showing the result in a clear matrix format.
The calculator supports 2x2 and 3x3 matrices, checks whether the matrix is invertible (non-singular), and uses the adjugate method for exact results.
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The inverse of a matrix A is a matrix A^(-1) such that A * A^(-1) = I (the identity matrix). A matrix has an inverse if and only if its determinant is non-zero.
For a 2x2 matrix [[a,b],[c,d]], the inverse is (1/det) * [[d,-b],[-c,a]] where det = ad - bc. For 3x3 matrices, the adjugate method or row reduction is used.
Aufgabe: Find the inverse of [[2, 1], [5, 3]]
Loesung: det = 2*3 - 1*5 = 1. Inverse = [[3, -1], [-5, 2]]
Antwort: [[3, -1], [-5, 2]]
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