Find the determinant, trace and inverse of a two-by-two matrix.
Understanding the matrix calculation
Enter the four entries of a 2×2 matrix and this calculator returns its determinant, trace, whether it’s invertible, and the inverse matrix.
These are the core operations for solving small linear systems.
Try it with these numbers
On the values this calculator opens with, the determinant is 10. Underneath, Trace comes out at 10 and Invertible? at Yes. Change any field and every figure updates as you type.
How to use it
- Enter the top row a and b.
- Enter the bottom row c and d.
- Read the determinant, trace and inverse.
The calculation
determinant = ad − bc
inverse = 1/det × [d, −b; −c, a]
Questions people ask about this
What is a determinant?
A single number describing a matrix. For 2×2 it’s ad − bc; if it’s zero, the matrix has no inverse.
When is a matrix invertible?
When its determinant is non-zero. A zero determinant means the matrix is singular.
What is the trace?
The sum of the diagonal entries, a + d for a 2×2 matrix.