2. suppose that t is an invertible linear transformation on v, in the sense that there is a linear transformation s : v-v such that t(s(v)) s(t(v)) = v for all v in v. (this generalizes the definition given in section 2.3 for v-r") the transformation s is denoted by t-1. let b - [bi, , bn) be a basis for v. show that the b-matrix for t is invertible and that the inverse of this matrix is [t this proves one implication in the theorem. to prove the other half, suppose that t: v-> v is a linear transformation with an invertible b-matrix t8. define s : vvin the following way. let v be in v, and let x [t]bimb. if t1 t2 define 3. show that s is a linear transformation. 4. show that t(s(v) v for all v in v by showing that [t(s(v)b vb 5. show that s(t(v)-v for all v in v by showing that is(t(v))|b-|v1b.