= Solution
Let $E_{12}=\begin{pmatrix}0&1\\0&0\end{pmatrix}$, so $A(t)=I+tE_{12}$ and $E_{12}^2=0$. Multiplication gives
$$
\begin{pmatrix}m&0\\0&m^{-1}\end{pmatrix}
A(t)
\begin{pmatrix}m^{-1}&0\\0&m\end{pmatrix}
=\begin{pmatrix}1&m^2t\\0&1\end{pmatrix}.
$$
The nilpotence also gives $(I+tE_{12})^k=I+ktE_{12}$ for every nonnegative integer $k$, since all higher binomial terms vanish. Hence, for each positive integer $m$,
$$
\boxed{\operatorname{diag}(m,m^{-1})A(t)\operatorname{diag}(m,m^{-1})^{-1}
=A(m^2t)=A(t)^{m^2}.}
$$
These are <unipotent matrices> in <SL2R>. The integer is positive, since the displayed diagonal <matrix> is undefined at $m=0$.
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