Of a 2×2 matrix:
detA = a1b2 - a2b1.
Of a 3×3 matrix:
detA = (a1b2c3 + b1c2a3 + c1a2b3) - (a3b2c1 + b3c2a1 + c3a2b1)
Cramer's Rule states that:
x =where D is the 3×3 coefficient matrix, and Dx, Dy, and Dz are each the result of substituting the constant column for one of the coefficient columns in D.