csat-suneung 2007 Q12

csat-suneung · South-Korea · csat__math-science 3 marks
Two square matrices $A , B$ of order 2 satisfy $A ^ { 2 } = E , B ^ { 2 } = B$. Which of the following statements in are always correct? (Here, $E$ is the identity matrix.) [3 points]
Remarks ㄱ. If matrix $B$ has an inverse, then $B = E$. ㄴ. $( E - A ) ^ { 5 } = 2 ^ { 4 } ( E - A )$ ㄷ. $( E - A B A ) ^ { 2 } = E - A B A$
(1) ㄱ
(2) ㄷ
(3) ㄱ, ㄴ
(4) ㄴ, ㄷ
(5) ㄱ, ㄴ, ㄷ
Two square matrices $A , B$ of order 2 satisfy $A ^ { 2 } = E , B ^ { 2 } = B$. Which of the following statements in <Remarks> are always correct?
(Here, $E$ is the identity matrix.) [3 points]

\textbf{Remarks}\\
ㄱ. If matrix $B$ has an inverse, then $B = E$.\\
ㄴ. $( E - A ) ^ { 5 } = 2 ^ { 4 } ( E - A )$\\
ㄷ. $( E - A B A ) ^ { 2 } = E - A B A$\\
(1) ㄱ\\
(2) ㄷ\\
(3) ㄱ, ㄴ\\
(4) ㄴ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ