csat-suneung 2010 Q13

csat-suneung · South-Korea · csat__math-humanities 4 marks Matrices Matrix Algebra and Product Properties

For a $2 \times 2$ square matrix $A$ and matrix $B = \left( \begin{array} { l l } 1 & 0 \\ 1 & 1 \end{array} \right)$ such that $( B A ) ^ { 2 } = \left( \begin{array} { l l } 1 & 1 \\ 1 & 2 \end{array} \right)$, what is the matrix $( A B ) ^ { 2 }$? [4 points]
(1) $\left( \begin{array} { l l } 1 & 1 \\ 1 & 2 \end{array} \right)$
(2) $\left( \begin{array} { l l } 2 & 1 \\ 1 & 2 \end{array} \right)$
(3) $\left( \begin{array} { l l } 2 & 1 \\ 1 & 1 \end{array} \right)$
(4) $\left( \begin{array} { l l } 1 & 2 \\ 2 & 1 \end{array} \right)$
(5) $\left( \begin{array} { l l } 1 & 1 \\ 2 & 1 \end{array} \right)$

For a $2 \times 2$ square matrix $A$ and matrix $B = \left( \begin{array} { l l } 1 & 0 \\ 1 & 1 \end{array} \right)$ such that $( B A ) ^ { 2 } = \left( \begin{array} { l l } 1 & 1 \\ 1 & 2 \end{array} \right)$, what is the matrix $( A B ) ^ { 2 }$? [4 points]\\
(1) $\left( \begin{array} { l l } 1 & 1 \\ 1 & 2 \end{array} \right)$\\
(2) $\left( \begin{array} { l l } 2 & 1 \\ 1 & 2 \end{array} \right)$\\
(3) $\left( \begin{array} { l l } 2 & 1 \\ 1 & 1 \end{array} \right)$\\
(4) $\left( \begin{array} { l l } 1 & 2 \\ 2 & 1 \end{array} \right)$\\
(5) $\left( \begin{array} { l l } 1 & 1 \\ 2 & 1 \end{array} \right)$

Paper Questions

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