Exercise 7, § 11

Algebra, III, 648

With the hypotheses and notation of Proposition 11 (no. 9), prove the formula

(\det g)\phi^{-1} = \bigwedge(g) \circ \phi^{-1} \circ \bigwedge^{(t_g)}.

Form this formula and (79) (no. 11) derive a new proof of the expression for the inverse of a square matrix using the matrix of its cofactors (§ 8, no. 6, formula (26)).

Solution

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