- #36

Hall

- 351

- 88

If A (n x n dimension) is the coefficient matrix for T:V_n -> V_n , T is a Linear transformation and the columns of A represent the coefficients of the basis elements of range V_n when T is applied to one of the basis elements of domain V_n.

Prove that A is invertible if and only if T is invertible. And then prove that the inverse of A is the coefficient matrix of ##T^{-1}##.