Mathematics

Mathematics

Problem

Consider the matrices P=[02−1130−214],Q=[5−1204310−2].P=\begin{bmatrix}0 & 2 & -1\\1 & 3 & 0\\-2 & 1 & 4\end{bmatrix},\quad Q=\begin{bmatrix}5 & -1 & 2\\0 & 4 & 3\\1 & 0 & -2\end{bmatrix}. Find both the products PQPQ and QPQP. State clearly whether PQ=QPPQ=QP or PQ≠QPPQ\neq QP, giving complete calculations to support your conclusion.

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