$If space straight A equals open square brackets table row 0 cell space space space 0 end cell cell space space 1 end cell row 0 cell space space 1 end cell cell space space 0 end cell row 1 cell space space 0 end cell cell space space 0 end cell end table close square brackets space comma$ find A². Hence find the matrix A⁶.

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Solution

Here space straight A equals open square brackets table row 0 cell space space 0 end cell cell space space 1 end cell row 0 cell space space 1 end cell cell space space 0 end cell row 1 cell space space 0 end cell cell space space 0 end cell end table close square brackets therefore space space straight A squared equals space AA equals open square brackets table row 0 cell space space 0 end cell cell space space 1 end cell row 0 cell space space 1 end cell cell space space 0 end cell row 1 cell space space 0 end cell cell space space 0 end cell end table close square brackets open square brackets table row 0 cell space space 0 end cell cell space space 1 end cell row 0 cell space space 1 end cell cell space space 0 end cell row 1 cell space space 0 end cell cell space space 0 end cell end table close square brackets space space space space equals open square brackets table row cell 0 plus 0 plus 1 end cell cell space space 0 plus 0 plus 0 end cell cell space space 0 plus 0 plus 0 end cell row cell 0 plus 0 plus 0 end cell cell space space 0 plus 1 plus 0 end cell cell space space 0 plus 0 plus 0 end cell row cell 0 plus 0 plus 0 end cell cell space space 0 plus 0 plus 0 end cell cell space space 1 plus 0 plus 0 end cell end table close square brackets space equals open square brackets table row 0 cell space space 0 end cell cell space space 1 end cell row 0 cell space space 1 end cell cell space space 0 end cell row 1 cell space space 0 end cell cell space space 0 end cell end table close square brackets equals 1 NOW space straight A to the power of 6 space equals left parenthesis straight A squared right parenthesis cubed space equals left parenthesis 1 right parenthesis cubed equals 1 therefore space straight A to the power of 6 space equals open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets

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Matrices

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Matrices

find A2. Hence find the matrix A6.

Some More Questions From Matrices Chapter

If a matrix has 8 elements, what arc the possible orders it can have ?

If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?

If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

If a matrix A has 12 elements, what arc the possible orders it can have 7 What if it has 7 elements ?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation