Linear Algebra
Determinant of a 2x2 matrix
The difference of the diagonal product and the off-diagonal product.
The Formula
det(A) = a x d - b x c
The difference of the diagonal product and the off-diagonal product.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| det(A) | Determinant | none | A single number that decides invertibility. |
| a, d | Diagonal entries | none | The top-left and bottom-right entries. |
| b, c | Off-diagonal entries | none | The top-right and bottom-left entries. |
What Each Symbol Means
det(A)none
Determinant
A single number that decides invertibility.
a, dnone
Diagonal entries
The top-left and bottom-right entries.
b, cnone
Off-diagonal entries
The top-right and bottom-left entries.
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.