Theorem: Cauchy-Binet residual det(A A^T) - sum det(A_S)^2 = 0 (2x3 UCF test matrix)

Theorem (UCF Cauchy-Binet identity canonical): for any real 2 x 3 matrix A with rows a = (a_11, a_12, a_13), a' = (a_21, a_22, a_23), the difference det(A A^T) - sum_{|S|=2} det(A_S)^2 evaluates identically to 0 as a polynomial in the six…