Question

Let
$A=\begin{pmatrix} 1 & 1 & 0 & 0 & 1 \\\ 1 & 1 & 1 & 1 & 3 \\\ 1 & 1 & 4 & 4 &4 \\\ \end{pmatrix}$
and B be a 5 × 5 real matrix such that AB is the zero matrix. Then the maximum possible rank of B is equal to ____________.

Answer 1

The correct answer is 2.