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Matrix Identity (Posted on 2007-04-26) Difficulty: 2 of 5
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.

See The Solution Submitted by Brian Smith    
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Solution re: Solution | Comment 2 of 8 |
(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
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