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Let V and W be vector spaces and let T:V→W be a linear transformation. We say...

Let V and W be vector spaces and let T:V→W be a linear transformation. We say a linear transformation S:W→V is a left inverse of T if ST=Iv, where ?v denotes the identity transformation on V. We say a linear transformation S:W→V is a right inverse of ? if ??=?w, where ?w denotes the identity transformation on W. Finally, we say a linear transformation S:W→V is an inverse of ? if it is both a left and right inverse of T . When T has an inverse, we say ? is invertible.

Show that

(a)  T has a right inverse iff T is surjective.

(b) If ? is a basis for ? and ? is a basis for ?, then [?]?? has a right inverse iff its rows are linearly independent.

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