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BITSAT2009MathematicsSequences and SeriesActual

If (A ) and (B ) are (2 2 ) matrices, then which of the following is true?

Options

  1. A(( A + B )^2= A ^2+ B ^2+2 AB )
  2. B((A-B)^2=A^2+B^2-2 A B )
  3. C((A-B)(A+B)=A^2+A B-B A-B^2 )
  4. D((A-B)(A+B)=A^2-B^2 )

Correct answer

C. ((A-B)(A+B)=A^2+A B-B A-B^2 )

Step-by-step solution

For two (2 2 ) matrices, (A ~ &~ B ) ( aligned & (A-B) (A+B) & =A A+A B-B A-B B & =A^2-B^2+A B-B A aligned ) Hence, ((A-B)(A+B)=A^2+A B-B A-B^2 )

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