Linear Algebra
Verifying an inverse
Multiply the original matrix by the claimed inverse; the answer must be the identity.
The Formula
A x A inverse = I, the identity matrix
Multiply the original matrix by the claimed inverse; the answer must be the identity.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| A | Original matrix | none | The matrix being inverted. |
| A inverse | Claimed inverse | none | The result to be checked. |
| I | Identity matrix | none | Ones on the diagonal and zeroes elsewhere. |
What Each Symbol Means
Anone
Original matrix
The matrix being inverted.
A inversenone
Claimed inverse
The result to be checked.
Inone
Identity matrix
Ones on the diagonal and zeroes elsewhere.
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.