Mathematics

Problem

Let

M=\begin{pmatrix}1&2&0\\0&1&0\\0&0&1\end{pmatrix}

and

N=\begin{pmatrix}1&-2&0\\0&1&0\\0&0&1\end{pmatrix}

. Consider the products

MN

and

NM

. Which statement is correct? a)

MN=I_3

but

NM\ne I_3

MN=M

and

NM=N

c) Both

MN

and

NM

are equal to

I_3

NM=I_3

but

MN\ne I_3