Find $A ^ { 80 }$ when $A = \left[ \begin{array} { l l l }
0 & 1 & 1 \
0 & 0 & 1 \
0 & 0 & 0
\end{array} \right]$ .
A) $\left[ \begin{array} { l l l }
1 & 0 & 0 \
0 & 1 & 0 \
0 & 0 & 1
\end{array} \right]$
B) $[ 0 ]$
C) $\left[ \begin{array} { l l l }
0 & 0 & 0 \
0 & 0 & 0 \
0 & 0 & 0
\end{array} \right]$
D) $\left[ \begin{array} { l l l }
1 & 1 & 1 \
1 & 1 & 1 \
1 & 1 & 1
\end{array} \right]$
E) $[ 1 ]$

Question

Find $A ^ { 80 }$ when $A = \left[ \begin{array} { l l l } 
0 & 1 & 1 \
0 & 0 & 1 \
0 & 0 & 0
\end{array} \right]$ .  
A) $\left[ \begin{array} { l l l } 
1 & 0 & 0 \
0 & 1 & 0 \
0 & 0 & 1
\end{array} \right]$
B) $[ 0 ]$
C) $\left[ \begin{array} { l l l } 
0 & 0 & 0 \
0 & 0 & 0 \
0 & 0 & 0
\end{array} \right]$
D) $\left[ \begin{array} { l l l } 
1 & 1 & 1 \
1 & 1 & 1 \
1 & 1 & 1
\end{array} \right]$
E) $[ 1 ]$

Quizplus · Accepted Answer

Matrix $A$ is a strictly upper triangular matrix. When such a matrix is raised to a power equal to or greater than its size (in this case, 3), the result is the zero matrix. Thus, $A^{80}$ will also be a zero matrix.

Find A80A ^ { 80 }A80 When A=[011001000]A = \left[ \begin{array} { l l l } 0 & 1 & 1 \\0 & 0 & 1 \\0 & 0 & 0\end{array} \right]A=​000​100​110​​

Find $A ^ { 80 }$ When $A = \left[ \begin{array} { l l l } 0 & 1 & 1 \\0 & 0 & 1 \\0 & 0 & 0\end{array} \right]$