Math — 3×3 Determinant & Cramer's Rule

\det A = a(ei - fh) - b(di - fg) + c(dh - eg)

x_i = \frac{\det A_i}{\det A}

A^{-1} = \frac{1}{\det A}\operatorname{adj}(A)

\det A \neq 0 \Rightarrow \text{invertible}