Matrix Determinant Calculator
Enter a square 2x2 or 3x3 matrix and instantly see its determinant with the full cofactor expansion.
2x2 matrix
- 1
Product a·d
1 × 4 = 4 - 2
Product b·c
2 × 3 = 6 - 3
Determinant
4 − 6 = -2
How does this calculator work?
The determinant of a 2×2 matrix is a·d − b·c, and of a 3×3 matrix it is a(ei−fh) − b(di−fg) + c(dh−eg). Enter your square matrix one row per line; the tool detects the size, computes the value, and flags whether the matrix is invertible (nonzero determinant).
Formula
How this is calculated
Type your matrix one row per line, separating numbers with spaces or commas. The calculator counts the rows to detect the matrix size n and requires the matrix to be square (each row must have exactly n entries) with n equal to 2 or 3; any other shape returns no result.
For a 2×2 matrix [[a,b],[c,d]] the determinant is a·d − b·c. For a 3×3 matrix the calculator expands along the first row using the rule of Sarrus / cofactor expansion: det = a(ei−fh) − b(di−fg) + c(dh−eg). The bar chart shows the absolute size of each term so you can see which contributions dominate, and the equation card shows the signed expansion.
The determinant is unitless and scales linearly: multiplying any single row by a constant multiplies the determinant by that same constant. A determinant of exactly zero means the matrix is singular (its rows are linearly dependent) and therefore has no inverse, which is reported in the summary.
Frequently asked questions
Only square 2×2 and 3×3 matrices. The size is detected from the number of rows, and each row must contain that same number of values.
A zero determinant means the matrix is singular: its rows (or columns) are linearly dependent, so the matrix is not invertible and the corresponding linear system has no unique solution.
Put one row of the matrix on each line and separate the numbers in a row with spaces or commas, for example "1 2" on one line and "3 4" on the next.
Also known as
TG we-Calculate Editorial Team. (2026). Matrix Determinant Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/matrix-determinant-calculator
TG we-Calculate Editorial Team. "Matrix Determinant Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/matrix-determinant-calculator.
TG we-Calculate Editorial Team, "Matrix Determinant Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/matrix-determinant-calculator
@misc{wecalculate_matrix_determinant_calculator, title = {Matrix Determinant Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/matrix-determinant-calculator}}, year = {2026}, note = {TG we-Calculate} }
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