It is hard to answer a question like that when we do not know your definition of singular linear transformation or the theorems you know.

Try one of these:

1)Show the determinant of T is non zero by computing the matrix of T (fixing a basis) and then invert the matrix and then finally get inverse of T.

2)Show that T is one-one and onto. Let F be the inverse map, then . So compute F directly from that.

The second method is messy but it only uses definition of inverse.