Question: Here is an alternative proof of Cramer's Rule that doesn't overtly contain any geometry. Write Xi for the identity matrix with column i replaced by

Here is an alternative proof of Cramer's Rule that doesn't overtly contain any geometry. Write Xi for the identity matrix with column i replaced by the vector of unknowns x1, . . . , xn.
(a) Observe that AXi = Bi.
(b) Take the determinant of both sides.

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