How this calculator works
Choose a row or column and remove its row and column for each selected entry to form a minor matrix. Multiply each minor determinant by the checkerboard sign to obtain its cofactor, then multiply by the original entry. Summing the contributions gives the determinant. The table displays these steps for square matrices from 2 by 2 through 5 by 5. Decimal entries use floating-point arithmetic.
Formula
C_ij = (-1)^(i+j) det(M_ij). Along row i: det(A) = sum_j a_ij C_ij. A column expansion uses the corresponding column sum.
Worked example
For [[1,2],[3,4]], expanding the first row gives 1 times 4 + 2 times (-3) = -2. The diagonal matrix diag(2,3,4) has determinant 24.
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Frequently asked questions
Which row should I choose?
A row or column with many zeros reduces the number of non-zero contributions. Every choice gives the same determinant apart from rounding.
Where do cofactor signs start?
The top-left sign is positive, with signs alternating across each row and down each column.
Can a singular matrix be entered?
Yes. Its determinant is zero in exact arithmetic; nearly singular decimal matrices can show small rounding residuals.