Matrix A is given by A=61124 then the determinant of A2015−6A2014 is

|A2015−6A2014|=|A|2014|A−6I|= 22014|0112−2|=(−22)22014=−11(2)2015

Matrix A is given by A=61124 then the determinant of A2015−6A2014 is

|A2015−6A2014|=|A|2014|A−6I|= 22014|0112−2|=(−22)22014=−11(2)2015

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Matrix A is given by $A = [\begin{array}{r} 6 & 11 \\ 2 & 4 \end{array}]$ then the determinant of $A^{2015} - 6 A^{2014}$ is

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$2^{2016}$

$(- 11) 2^{2015}$

$- 2^{2015} \times 7$

$(- 9) 2^{2014}$

answer is B.

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Detailed Solution

$| A^{2015} - 6 A^{2014} | = {| A |}^{2014} | A - 6 I | = 2^{2014} | \begin{array}{r} 0 & 11 \\ 2 & - 2 \end{array} | = (- 22) 2^{2014} = - 11 {(2)}^{2015}$

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Matrix A is given by A=61124 then the determinant of A2015−6A2014 is

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Matrix A is given by $A = [\begin{array}{r} 6 & 11 \\ 2 & 4 \end{array}]$ then the determinant of $A^{2015} - 6 A^{2014}$ is