Question

$If space straight A space is space square space matrix space such space that space straight A squared equals space straight A comma space then space left parenthesis straight I space plus space straight A right parenthesis cubed space – space 7 straight A space is space equal space to space left parenthesis straight A right parenthesis space straight A space comma space left parenthesis straight B right parenthesis space straight I – space straight A space left parenthesis straight C right parenthesis space 1 space left parenthesis straight D right parenthesis space 3 straight A$

Solution

We space have space straight A squared space equals straight A space space space space space space space space space space space space space space space space space space space space space space space space space space.... left parenthesis 1 right parenthesis therefore space space straight A cubed space equals space space straight A squared space. straight A space equals straight A space. straight A space equals straight A to the power of 2 space end exponent space equals space straight A space space... left parenthesis 2 right parenthesis now space space left parenthesis space straight I plus straight A right parenthesis space minus 7 straight A space equals space left parenthesis straight I plus 3 straight A plus 3 straight A to the power of 2 space end exponent space plus space space straight A cubed space right parenthesis space minus 7 straight A space space space space open square brackets table row cell because space of space left parenthesis 1 right parenthesis space end cell end table close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space left parenthesis straight I plus 3 space straight A plus 3 space straight A space plus to the power of space space space straight A space right parenthesis space minus 7 straight A space space space space space open square brackets table row cell because space of space left parenthesis 1 right parenthesis space. space left parenthesis 2 right parenthesis end cell end table close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space straight I therefore space left parenthesis straight C right parenthesis space space is space correct space answer. space space space space space space space space space space space space space space space

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Matrices

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