csat-suneung 2015 Q19

csat-suneung · South-Korea · csat__math-A 4 marks Matrices True/False or Multiple-Select Conceptual Reasoning
Two $2 \times 2$ square matrices $A$ and $B$ satisfy $$A ^ { 2 } - A B = 3 E , \quad A ^ { 2 } B - B ^ { 2 } A = A + B$$ Among the statements in the given options, which are correct? (Here, $E$ is the identity matrix.) [4 points]
ᄀ. The inverse matrix of $A$ exists. ㄴ. $A B = B A$ ㄷ. $( A + 2 B ) ^ { 2 } = 24 E$
(1) ᄀ
(2) ᄃ
(3) ᄀ, ᄂ
(4) ᄂ, ᄃ
(5) ᄀ, ᄂ, ᄃ 
Two $2 \times 2$ square matrices $A$ and $B$ satisfy
$$A ^ { 2 } - A B = 3 E , \quad A ^ { 2 } B - B ^ { 2 } A = A + B$$
Among the statements in the given options, which are correct? (Here, $E$ is the identity matrix.) [4 points]

ᄀ. The inverse matrix of $A$ exists.\\
ㄴ. $A B = B A$\\
ㄷ. $( A + 2 B ) ^ { 2 } = 24 E$\\
(1) ᄀ\\
(2) ᄃ\\
(3) ᄀ, ᄂ\\
(4) ᄂ, ᄃ\\
(5) ᄀ, ᄂ, ᄃ
Paper Questions
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