document.write( "Question 1103091: Demonstrate, using a counter example, that the product of two isometries P and Q is not always commutative (i.e., PQ does not always equal QP). \n" ); document.write( "

Algebra.Com's Answer #717802 by ikleyn(52794) $\"\"$ $\"About$

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document.write( "You can easily do it on your own by taking the parallel translation on 1 unit to the righ as an isometrie P on the 2D coordinate plane \r\n" );
document.write( "and taking the rotation to the angle 90 degs anticlockwise as an isometrie Q of the same 2D coordinate plane.\r\n" );
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document.write( "Then consider the image of the point (x,y) = (1,0) under PQ and under QP.\r\n" );
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