Q1. For A = [[2, 1], [3, 4]], find |A|.
|A| = ad − bc
= (2)(4) − (1)(3)
= 8 − 3 = 5
Matrices — Class 12
A matrix is just a rectangular array of numbers with its own algebra. Learn the operations and compute a determinant in one click.
Matrix & orderA rectangular array of numbers of order m × n (m rows, n columns).
Addition & scalar multiplicationAdd matrices of the same order element-wise; multiply every element by a scalar k.
Matrix multiplicationAB is defined only when columns of A = rows of B; it is generally NOT commutative (AB ≠ BA).
Transpose & symmetryAᵀ swaps rows and columns. A is symmetric if Aᵀ = A, skew-symmetric if Aᵀ = −A.
Determinant calculator Interactive
Enter a 2×2 or 3×3 matrix to compute its determinant with the expansion step.
Determinant value—
Solved examples
Formula sheet
| Quantity | Formula |
|---|---|
| Product condition | Aₘₓₙ · Bₙₓₚ = Cₘₓₚ |
| 2×2 determinant | ad − bc |
| Transpose | (Aᵀ)ᵢⱼ = Aⱼᵢ |
Common mistakes & exam wins
- Matrix multiplication is NOT commutative (AB ≠ BA in general).
- AB is defined only when the number of columns of A equals the number of rows of B.
- A determinant exists only for SQUARE matrices.
Frequently asked questions
When can two matrices be multiplied?
When the number of columns of the first equals the number of rows of the second.
What is the transpose of a matrix?
The matrix obtained by interchanging its rows and columns.
Is matrix multiplication commutative?
No — in general AB ≠ BA.