If matrix $A$ is given by $A = \begin{bmatrix} 6 & 11 \ 2 & 4 \end{bmatrix},$ then the determinant of$A^{2005} - 6A^{2004}$ is

Question

Dr. Abubacker · Accepted Answer

(b)
$\left| A^{2005} - 6A^{2004} ight| = |A|^{2004}|A - 6I|$
$2^{2004}\left| \begin{matrix}
0 & 11 \
2 & - 2
\end{matrix} ight| = ( - 22)2^{2004} = ( - 11)(2)^{2005}$

Q. If matrix $A$ is given by $A = \begin{bmatrix} 6 & 11 \\ 2 & 4 \end{bmatrix},$ then the determinant of$A^{2005} - 6A^{2004}$ is

Explanation

Reviewed by Dr. Abubacker

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