If A=pmatrix1&0&02&1&0-3&2&1pmatrix and B=pmatrix1&0&0-2&1&07&-2&1pmatrix, then AB equals

Question

If $A=\begin{pmatrix}1&0&0\2&1&0\-3&2&1\end{pmatrix}$ and $B=\begin{pmatrix}1&0&0\-2&1&0\7&-2&1\end{pmatrix}$, then $AB$ equals

Accepted Answer

Direct multiplication of the two lower-triangular unipotent matrices (which are inverses of each other by construction) gives $AB=I_3$.

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