csat-suneung 2015 Q16

csat-suneung · South-Korea · csat__math-B 4 marks Matrices True/False or Multiple-Select Conceptual Reasoning
Two square matrices $A , B$ satisfy $$A ^ { 2 } - A B = 3 E , \quad A ^ { 2 } B - B ^ { 2 } A = A + B$$ From the statements below, select all correct ones. (Here, $E$ is the identity matrix.) [4 points]
Statements 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 square matrices $A , B$ satisfy
$$A ^ { 2 } - A B = 3 E , \quad A ^ { 2 } B - B ^ { 2 } A = A + B$$
From the statements below, select all correct ones. (Here, $E$ is the identity matrix.) [4 points]

\textbf{Statements}\\
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