csat-suneung 2016 Q16

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

Statements\\
ㄱ. $A = B ^ { 2 }$\\
ㄴ. $B ^ { - 1 } = A ^ { 2 } + E$\\
ㄷ. $A ^ { 5 } - B ^ { 5 } = A + B$\\
(1) ㄱ\\
(2) ㄴ\\
(3) ㄱ, ㄷ\\
(4) ㄴ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ
Paper Questions
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q24 Q25 Q26 Q27 Q28 Q29 Q30