Trace, product of matricesMedium

Matrix Element Determination

Let A = [a_ij] be a 3 × 3 matrix such that
A $\left[ {\begin{array}{*{20}{c}} 0\\[0.9em] 1\\[0.9em] 0 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 0\\[0.9em] 0\\[0.9em] 1 \end{array}} \right],\,$ $A\left[ {\begin{array}{*{20}{c}} 4\\[0.9em] 1\\[0.9em] 3 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 0\\[0.9em] 1\\[0.9em] 0 \end{array}} \right]$ and $A\left[ {\begin{array}{*{20}{c}} 2\\[0.9em] 1\\[0.9em] 2 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 1\\[0.9em] 0\\[0.9em] 0 \end{array}} \right]$ , then a₂₃ equals:

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