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February 20th, 2010, 05:58 PM   #1
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T: V to V and [T]_B is invertible

let V be a finite-dimensional vector space with and ordered basis B and let T: V to V be linear.
Prove: If [T]_B is invertible then T is invertible. Furthermore, [T^-1]_B = ([T]_B)^-1
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