If I is the 2x2 identity matrix, show that there is an infinite number of matrices X with integer members such that X*X = I.

(In reply to Solution by hoodat)

In general:

( a   b )
( c  -a )

where bc = 1 - a^2 (therefore one of b or c will be positive, the other negative).

This includes:

( 1   0 )
( x  -1 )

where x is any integer.

For example, if a = 8 or 9, the following work (parens/braces not shown):

 8  1
-63 -8

 8  3
-21 -8

 8  7
-9 -8

 9  1
-80 -9

 9  2
-40 -9

 9  4
-20 -9

 9  5
-16 -9

 9  8
-10 -9

Posted by Charlie on 2007-04-26 09:49:05