Question

If $A=\left[\begin{array}{ccc}2& 0& 0\\ 0& 2& 0\\ 0& 0& 2\end{array}\right]$, then $A^6=$

• A. $6A$
• B. $12A$
• C. $16A$
• D. $32A$

Answer 1

Answer: (D)

$32A$

$A=\left[\begin{array}{ccc}2& 0& 0\\ 0& 2& 0\\ 0& 0& 2\end{array}\right]=2\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]=2I$

$\therefore A^6=(2I{)}^6=2^6\times I^6=2^{6}I$

$A^6=2^{6}I=2^5\left(2I\right)=2^{5}A=32A$