Identities, inverses and determinants for 2 x 2 matrices
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If \(X = \left[ {\begin{array}{*{20}{c}}{ - 2}\\1\end{array}} \right]\) and \(I = {\rm{ }}\left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right]\), find \(XI\) and \(IX.\)
\begin{align}
&\text{If } X=\left[\begin{array}{c}-2 \\ 1\end{array}\right] \text{ and }I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\\
&\text{Find } XI \text{ and } IX.\\
&XI=\left[\begin{array}{c}
-2 \\
1
\end{array}\right] \times\left[\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right]=\left[\begin{array}{c}
-2 \times 1+1 \times 0 \\
-2 \times 0+1 \times 1
\end{array}\right]=\left[\begin{array}{c}
-2 \\
1
\end{array}\right] \\
&IX=\left[\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right] \times\left[\begin{array}{c}
-2 \\
1
\end{array}\right]=\left[\begin{array}{c}
1\times -2+0 \times 1 \\
0 \times-2+1 \times 1
\end{array}\right]
=\left[\begin{array}{c}
-2 \\
1
\end{array}\right]
\end{align}
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