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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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Some Thoughts re(2): An Attempt To Generalisation Comment 8 of 8 |
(In reply to re: An Attempt To Generalisation by Brian Smith)


It is sufficient that  m Mod b = +/- 1 gives m^2 Mod b = 1.
However, the necessity part is NOT always true for any given m.
For example, if  m^2 Mod 12 = 1, then  m Mod 12 = +/- 5, +/-7, +/-1

This apparent discrepancy stemmed from the way the above step was presented in my previous post and I confirm having made the requisite amendments.

However, it may be observed that the statement inclusive of the general expression in my previous post did not claim that the said expression generates all possible integral values for a,b,c and d. 

Edited on May 1, 2007, 5:45 am
  Posted by K Sengupta on 2007-05-01 03:23:40

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