Question 1099338
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Give examples to show that the following statements are wrong.

1) if (Matrix) {{{A^2 = A}}}, then A = 0 or A is an Identity matrix
2) if AX = AY, and Y is not equal to 0, the X = Y
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<pre>
a)  Easiest counter-example:       A = {{{(matrix(2,2, 1,0,  1,0))}}}.


    Next easiest counter-example:  A = {{{(matrix(3,3, 1,0,0,  0,0,0, 0,0,1))}}}.


    Matrices with the property  {{{A^2}}} = A  are called <U>idempotent</U>.


    For further reading see, for example, this Wikipedia article

               https://en.wikipedia.org/wiki/Idempotent_matrix
</pre>

<pre>
b)  Easiest counter-example:       A = {{{(matrix(2,2, 1,0,  0,0))}}},  X = {{{(matrix(2,1, 1,0))}}},  Y = {{{(matrix(2,1, 1,2))}}}.   (where X and Y are vectors)


    Next easiest counter-example:  A = {{{(matrix(2,2, 1,0,  0,0))}}},  X = {{{(matrix(2,2, 1,0, 0,0))}}},  Y = {{{(matrix(2,2, 1,0, 0,1))}}}.


    You make all necessary calculations . . . 
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