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Question

Mathematics Question on Determinants

If A=[11−2\21−3\54−9]\begin{bmatrix}1&1&-2\\\2&1&-3\\\5&4&-9\end{bmatrix},find IAI.

Answer

Let A=[11−2\21−3\54−9]\begin{bmatrix}1&1&-2\\\2&1&-3\\\5&4&-9\end{bmatrix}
By expanding along the first row, we have:
IAI=1∣1−3\4−9∣−1∣2−3\5−9∣−2∣2−1\54∣1\begin{vmatrix}1&-3&\\\4&-9\end{vmatrix}-1\begin{vmatrix}2&-3&\\\5&-9\end{vmatrix}-2\begin{vmatrix}2&-1&\\\5&4\end{vmatrix}
=1(-9+12)-1(-18+15)-2(8-5)
=3+3-6
=6-6=0