csat-suneung 2012 Q15

csat-suneung · South-Korea · csat__math-humanities 4 marks Matrices True/False or Multiple-Select Conceptual Reasoning
Two $2 \times 2$ square matrices $A , B$ satisfy
$$A ^ { 2 } + B = 3 E , \quad A ^ { 4 } + B ^ { 2 } = 7 E$$
Which of the following statements are correct? (where $E$ is the identity matrix) [4 points]
ㄱ. $A B = B A$ ㄴ. $B ^ { - 1 } = A ^ { 2 }$ ㄷ. $A ^ { 6 } + B ^ { 3 } = 18 E$
(1) ㄱ
(2) ㄴ
(3) ㄱ, ㄴ
(4) ㄱ, ㄷ
(5) ㄱ, ㄴ, ㄷ 
Two $2 \times 2$ square matrices $A , B$ satisfy

$$A ^ { 2 } + B = 3 E , \quad A ^ { 4 } + B ^ { 2 } = 7 E$$

Which of the following statements are correct? (where $E$ is the identity matrix) [4 points]

<Statements>\\
ㄱ. $A B = B A$\\
ㄴ. $B ^ { - 1 } = A ^ { 2 }$\\
ㄷ. $A ^ { 6 } + B ^ { 3 } = 18 E$\\
(1) ㄱ\\
(2) ㄴ\\
(3) ㄱ, ㄴ\\
(4) ㄱ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ
Paper Questions
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