Q1. Evaluate the determinant [[1, 2], [3, 4]].
|A| = ad − bc
= (1)(4) − (2)(3)
= 4 − 6 = −2
Determinants — Class 12
The determinant tells you if a matrix is invertible and much more. Compute any 2×2 or 3×3 determinant instantly.
DeterminantA single number computed from a square matrix. For 2×2 [[a,b],[c,d]] it is ad − bc.
Minors & cofactorsDelete the row and column of an element to get its minor; the cofactor adds a (−1)ⁱ⁺ʲ sign.
Adjoint & inverseA⁻¹ = adj(A)/|A|, valid only when |A| ≠ 0 (non-singular matrix).
Cramer's ruleSolves a system of linear equations using ratios of determinants.
Determinant calculator Interactive
Enter a 2×2 or 3×3 matrix and read off its determinant, with the expansion.
Determinant value—
Solved examples
Formula sheet
| Quantity | Formula |
|---|---|
| 2×2 determinant | |A| = ad − bc |
| Inverse | A⁻¹ = adj(A) / |A| |
| Area of triangle | ½ |determinant of coordinates| |
| Singular matrix | |A| = 0 ⇒ no inverse |
Common mistakes & exam wins
- A matrix is invertible only if its determinant is non-zero (|A| ≠ 0).
- Swapping two rows changes the sign of the determinant.
- If any row/column is all zeros, or two are identical, the determinant is 0.
Frequently asked questions
How do you find the determinant of a 2×2 matrix?
For [[a, b], [c, d]], the determinant is ad − bc.
When is a matrix invertible?
When its determinant is non-zero; then A⁻¹ = adj(A)/|A|.
What does a determinant of zero mean?
The matrix is singular — it has no inverse (and the rows/columns are linearly dependent).