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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 Problem solution | Comment 4 of 8 |

      | m    1+m |
X = 
      | 1-m   -m  |

whenever m is an integer, with |m| != 1, satisfies all the conditions of the given problem.

OR,

      | 1-t      2-t | 
X = 
      | t         t-1 |

whenever t is an integer , with  t! = 0, 2 also satisfies all conditions of the given problemsatisfy conditions of the problem.

 

Edited on April 27, 2007, 2:58 pm
  Posted by K Sengupta on 2007-04-27 03:09:52

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