I need to find all 2x2 matrices A,

(a b)

(c d)

such that A^2=I2, the 2x2 identity matrix.

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- Feb 19th 2009, 06:26 PMSnooks02Matrices which are their own inverses
I need to find all 2x2 matrices A,

(a b)

(c d)

such that A^2=I2, the 2x2 identity matrix. - Feb 19th 2009, 09:15 PMtah
this means that A is equal to its inverse. So you may write the expression of $\displaystyle A^{-1}$ and deduce 4 equations from the identification of it with A. It remains to solve these equations

- Feb 19th 2009, 09:57 PMJhevon
Just to flesh out what

**tah**said:

you have $\displaystyle \begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} a & b \\ c & d \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$

now, compute the matrix product on the left hand side, then equate corresponding components to get your 4 equations that**tah**spoke of. solve this system for your solution - Feb 19th 2009, 10:51 PMmath2009
$\displaystyle A=\begin{bmatrix} a&b \\ \frac{1-a^2}{b} &-a \end{bmatrix}\ or\ \pm I_2$