Mathematics

Problem

Identify the pair of non-zero

2\times2

matrices

(A,B)

for which

AB = O_2

but

BA \ne O_2

. a)

A=\begin{bmatrix}1&0\\0&0\end{bmatrix},\;B=\begin{bmatrix}0&1\\0&0\end{bmatrix}

A=\begin{bmatrix}1&0\\0&0\end{bmatrix},\;B=\begin{bmatrix}0&0\\0&1\end{bmatrix}

A=\begin{bmatrix}0&1\\0&0\end{bmatrix},\;B=\begin{bmatrix}1&0\\0&0\end{bmatrix}

A=\begin{bmatrix}1&0\\0&1\end{bmatrix},\;B=\begin{bmatrix}0&1\\0&0\end{bmatrix}