I need some help on this question and a couple explanations on some terms.

$\displaystyle A= \left(\begin{array}{cc}k&-2\\1-k&k\end{array}\right)$, where k is a constant.

A transformation $\displaystyle T: \Re^2 \rightarrow \Re^2$ is represented by the matrixA.

a) Find the value of k for which the line y=2x is mapped onto itself under T

b) show thatAis non-singular for all values of k

i need help on both parts of the question, and waht is ment by non-singular?