The matrix I is its own inverse, since I•I=I
1. Find two second order matrices (other than I) that have this property.
2. If A=A^-1, show that det A = +/-1.
Any suggestions? Thanks,
Newt
2. If A=A^-1, show that det A = +/-1.
Any suggestions? Thanks,
$\displaystyle \left| {A^{ - 1} } \right| = \frac{1}
{{\left| A \right|}}
$
therefore if:
$\displaystyle
\begin{gathered}
\left| A \right| = \frac{1}
{{\left| A \right|}} \hfill \\
\Leftrightarrow \left| A \right|^2 = 1 \hfill \\
\Leftrightarrow \left| A \right| = \pm 1 \hfill \\
\end{gathered} $