Prove that $A=\left(\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right)$ is not invertible $$A=\left(\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right)$$
I don't know how to start. Will be grateful for a clue.
Edit: Matrix ranks and Det have not yet been presented in the material.

Row operations or column operationas don't change the rank of the matrix. So it is invertible iff anything row/column equivalent to it is invertible. 
Subtract 1 times the second column  from the third, 1 times the first column from the second column; this gives $$\begin{pmatrix} 1&1&1\\ 4&1&1 \\7&1&1\end{pmatrix}.$$
This is clearly singular since two columns are equal.
