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sci.matrix-determinant-2x2 Calculator
Calculates the determinant of a 2×2 matrix: det(A) = ad − bc, and uses it to determine invertibility and solve 2×2 linear systems by Cramer's rule. det(A) = 0 means the matrix is singular (no unique inverse) — the system Ax = b has no solution or infinitely many solutions.
Inputs
A11
Reference formula or conversion factor shown for context.
A12
Reference formula or conversion factor shown for context.
A21
Reference formula or conversion factor shown for context.
A22
Reference formula or conversion factor shown for context.
Results
determinant |A|
A single number summarising key properties of a matrix. Non-zero: the system has a unique solution. Zero (singular matrix): no unique solution exists.
trace tr(A)
Reference formula or conversion factor shown for context.
invertible?
Sample size or count used in the calculation.
A⁻¹[1,1] = d/det
Reference formula or conversion factor shown for context.
A⁻¹[1,2] = -b/det
Reference formula or conversion factor shown for context.
det = ad - bc
Reference formula or conversion factor shown for context.