Inverse Matrix question

**Jim Newt** · March 17th 2008, 12:39 PM

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

**Moo** · March 17th 2008, 12:45 PM

Hello,

Try :
10
01

01
10

**Peritus** · March 17th 2008, 01:28 PM

2. If A=A^-1, show that det A = +/-1.

Any suggestions? Thanks,

$\left| {A^{ - 1} } \right| = \frac{1} {{\left| A \right|}} $

therefore if:
$ \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}$

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