csat-suneung 2006 Q6

csat-suneung · South-Korea · csat__math-humanities 3 marks Matrices Matrix Algebra and Product Properties

For all non-zero $2 \times 2$ square matrices $A , B$ satisfying the following three conditions, which matrix is always equal to $B ^ { 3 } + 2 B A ^ { 3 }$? (Here, $E$ is the identity matrix.) [3 points] (가) $A B = B A$ (나) $( E - B ) ^ { 2 } = E - B$ (다) $A B = - B$
(1) $2 A$
(2) $- A$
(3) $E$
(4) $2 B$
(5) $- B$

For all non-zero $2 \times 2$ square matrices $A , B$ satisfying the following three conditions, which matrix is always equal to $B ^ { 3 } + 2 B A ^ { 3 }$? (Here, $E$ is the identity matrix.) [3 points]\\
(가) $A B = B A$\\
(나) $( E - B ) ^ { 2 } = E - B$\\
(다) $A B = - B$\\
(1) $2 A$\\
(2) $- A$\\
(3) $E$\\
(4) $2 B$\\
(5) $- B$

Paper Questions

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