Without multiplying matrices, find bases for the row and column spaces of A:

$\displaystyle A=\left[ {\begin{array}{cc}1 & 2 \\4 & 5 \\2 & 7 \\ \end{array} } \right]\left[ {\begin{array}{ccc}3 & 0 & 3 \\1 & 1 & 2 \\\end{array} } \right]$

How do you know from these shapes that A cannot be invertible?