What is invertible linear transformation?

a linear transformation is invertible iff it's a non singular matrix.

non singular means non zero determinant..

make a transformation matrix with respect to basis , if that matrix's determinant is non zero ..

go through this video , it will help you. https://youtu.be/5ef0Ux9OEdc

a linear transformation T from V into W is said to be invertible if and only if it is bijective when viewed as a function from V into W