Matrix Inverse Calculator
2×2 Matrix Inverse
Find the inverse of a 2×2 matrix using the adjugate formula
3×3 Matrix Inverse
Find the inverse of a 3×3 matrix
Formula
2×2: A⁻¹ = (1/det)[[d,-b],[-c,a]] | 3×3: A⁻¹ = adj(A)/det(A)
Frequently Asked Questions
What is a matrix inverse?
The inverse of a matrix A, written A⁻¹, is the matrix such that A × A⁻¹ = I (the identity matrix). Only square matrices with non-zero determinants have inverses.
How do you find the inverse of a 2×2 matrix?
For [[a,b],[c,d]], the inverse is (1/det) × [[d,-b],[-c,a]] where det = ad - bc. If det = 0, the matrix is singular and has no inverse.
You may also need
+
Matrix Calculator
Free matrix calculator. Calculate the determinant, inverse, and transpose of 2×2 and 3×3 matrices.
Math+
Eigenvalue Calculator
Free eigenvalue and eigenvector calculator. Find eigenvalues and eigenvectors of 2x2 and 3x3 matrices with step-by-step solutions.
Math+
Determinant Calculator
Free determinant calculator. Calculate the determinant of 2x2 and 3x3 matrices.
Math