$If space straight A equals open square brackets table row 2 cell space minus 1 end cell row 3 cell space space space space 1 end cell end table close square brackets space comma space straight B equals space open square brackets table row 1 cell space space 3 end cell row 2 cell space 1 end cell end table close square brackets$ verify that (A + B) (A – B) ≠ A² – B².

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Solution

Here space straight A equals space open square brackets table row 2 cell space minus 1 end cell row 3 cell space space space space space space 1 end cell end table close square brackets space comma space straight B equals open square brackets table row 1 cell space space 3 end cell row 2 cell space space 1 end cell end table close square brackets therefore space straight A plus straight B space equals space open square brackets table row cell 2 plus 1 end cell cell space minus 1 plus 3 end cell row cell 3 plus 2 end cell cell space space space space space 1 plus 1 end cell end table close square brackets space equals space open square brackets table row 3 cell space space space 2 end cell row 5 cell space space 2 end cell end table close square brackets space space straight A minus straight B space equals open square brackets table row cell 2 minus 1 end cell cell space minus 1 minus 3 end cell row cell 3 minus 2 end cell cell space space space space space 1 minus 1 end cell end table close square brackets equals open square brackets table row 1 cell space minus 4 end cell row 1 cell space space space space 0 end cell end table close square brackets therefore space left parenthesis straight A plus straight B right parenthesis left parenthesis straight A minus straight B right parenthesis space equals space open square brackets table row cell 3 space end cell cell space space space 2 end cell row 5 cell space space 2 end cell end table close square brackets space open square brackets table row 1 cell space minus 4 end cell row 1 cell space space space space space 0 end cell end table close square brackets equals open square brackets table row cell 3 plus 2 end cell cell space space minus 12 plus 0 end cell row cell 5 plus 2 end cell cell space space space minus 20 plus 0 end cell end table close square brackets equals open square brackets table row 5 cell space space minus 12 end cell row 7 cell space space minus 20 end cell end table close square brackets space... left parenthesis 1 right parenthesis space space space straight A to the power of 2 minus end exponent straight B squared space equals space open square brackets table row 2 cell space space minus 1 end cell row 3 cell space space space space space space space 1 end cell end table close square brackets space open square brackets table row 2 cell space minus 1 end cell row 3 cell space space space space 1 end cell end table close square brackets minus open square brackets table row 1 cell space space 3 end cell row 2 cell space space 1 end cell end table close square brackets space space space space space space space space space space space space space space equals open square brackets table row cell 4 minus 3 end cell cell negative 2 minus 1 end cell row cell 6 plus 3 end cell cell negative 3 plus 1 end cell end table close square brackets minus open square brackets table row cell 1 plus 6 end cell cell 3 plus 3 end cell row cell 2 plus 2 end cell cell 6 plus 1 end cell end table close square brackets space space space space space space space space space space space space space space equals space open square brackets table row 1 cell negative 3 end cell row 9 cell negative 2 end cell end table close square brackets minus open square brackets table row 7 6 row 4 7 end table close square brackets equals open square brackets table row cell 1 minus 7 end cell cell negative 3 minus 6 end cell row cell 9 minus 4 end cell cell negative 2 minus 7 end cell end table close square brackets equals open square brackets table row cell negative 6 end cell cell negative 9 end cell row 5 cell negative 9 end cell end table close square brackets space... left parenthesis 2 right parenthesis space space space space space space space space space space space space space From space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis comma space left parenthesis straight A space plus space straight B right parenthesis space left parenthesis straight A space – space straight B right parenthesis space not equal to space straight A squared space – space straight B squared

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verify that (A + B) (A – B) ≠ A2 – B2.

Some More Questions From Matrices Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation