Linear Algebra
Inverse of a 2x2 matrix
Swap the diagonal, negate the off-diagonal, divide by the determinant.
The Formula
A inverse = (1 / det(A)) x [ d, -b; -c, a ]
Swap the diagonal, negate the off-diagonal, divide by the determinant.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| A inverse | Inverse matrix | none | The matrix that undoes A. |
| det(A) | Determinant | none | ad minus bc, which must not be zero. |
| a, b, c, d | Entries of A | none | The four entries in row order. |
What Each Symbol Means
A inversenone
Inverse matrix
The matrix that undoes A.
det(A)none
Determinant
ad minus bc, which must not be zero.
a, b, c, dnone
Entries of A
The four entries in row order.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate the inverse of a matrix page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate The Inverse Of A Matrix, filed under Math. Every number the guide produces comes from substituting into this one line.