Calculates the inverse of a 2x2 or 3x3 square matrix. The inverse matrix is calculated if it exists. If the determinant is zero, the matrix is not invertible.
Start with your values, or try a preset.
Enter Matrix Size, a11, a12, a21, a22, a13, a23, a31, a32, and a33 in the units shown.
Read Determinant (3x3), Determinant (2x2), Inverse Exists?, Inverse a33, Inverse a32, Inverse a31, Inverse a23, Inverse a22, Inverse a21, Inverse a13, Inverse a12, and Inverse a11 in the results panel. Results update as you change the inputs.
Choose a preset to load an example, then adjust the values for your situation.
See the inputs and their calculated results.
Matrix Size: 2x2; a11: 1; a12: 0; a21: 0; a22: 1; a13: 0; a23: 0; a31: 0; a32: 0; a33: 1
Determinant (3x3): 1; Determinant (2x2): 1; Inverse Exists?: 1; Inverse a33: Matrix is not applicable; Inverse a32: Matrix is not applicable; Inverse a31: Matrix is not applicable; Inverse a23: Matrix is not applicable; Inverse a22: 1; Inverse a21: -0; Inverse a13: Matrix is not applicable; Inverse a12: -0; Inverse a11: 1
Matrix Size: 2x2; a11: 2; a12: 1; a21: 3; a22: 4; a13: 0; a23: 0; a31: 0; a32: 0; a33: 1
Determinant (3x3): 5; Determinant (2x2): 5; Inverse Exists?: 1; Inverse a33: Matrix is not applicable; Inverse a32: Matrix is not applicable; Inverse a31: Matrix is not applicable; Inverse a23: Matrix is not applicable; Inverse a22: 0.4; Inverse a21: -0.6; Inverse a13: Matrix is not applicable; Inverse a12: -0.2; Inverse a11: 0.8
Matrix Size: 3x3; a11: 1; a12: 0; a21: 0; a22: 1; a13: 0; a23: 0; a31: 0; a32: 0; a33: 1
Determinant (3x3): 1; Determinant (2x2): 1; Inverse Exists?: 1; Inverse a33: 1; Inverse a32: -1; Inverse a31: -1; Inverse a23: 0; Inverse a22: 1; Inverse a21: 0; Inverse a13: 0; Inverse a12: 0; Inverse a11: 1
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