A linear map that is multiplication by a matrix The problem statement, all given variables and data
Let $T$ be multiplication by matrix $A$:
$$A=
        \begin{bmatrix}
        1 & -1 & 3 \\
        5 & 6 & -4 \\
        7 & 4 & 2 \\
        \end{bmatrix}
$$
Find the range, kernel, rank and nullity of T.
Attempt at a solution
I can find all of these values except for A. What does the question mean when T is a multiplication by matrix A? How do I get range/kernel etc. of T.. I know how to get them for A.
Thanks.

It is a question of abstraction: $A$ is the matrix, the scheme, while $T$ is the transformation that multiplication with the matrix results in. $A$ and $T$ is not the same, specially since different matrices with respect to other basis can result in the same transformation.
