Show that the linear map defined by is non-singular and find its inverse.
Thanks in advance.
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.