document.write( "Question 1201590: prove that, for square matrices A and B, AB=BA if and only if(A-B)(A+B)=A²-B².
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Algebra.Com's Answer #836047 by ikleyn(52782) $\"\"$ $\"About$

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document.write( "(A-B)*(A+B) = A*A - B*A + A*B - B*B = (A^2 - B^2) + (A*B - B*A).\r\n" );
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document.write( "From this identity, which is valid for all matrices ALWAYS,  you can easily conclude that  \r\n" );
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document.write( "    (A-B)*(A+B) = A^2 - B^2  if and only if  A*B - B*A = 0.\r\n" );
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document.write( "It is the same as to say that \r\n" );
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document.write( "    (A-B)*(A+B) = A^2 - B^2  if and only if  A*B = B*A.\r\n" );
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