csat-suneung 2005 Q6

csat-suneung · South-Korea · csat__math-humanities 3 marks Matrices Matrix Algebra and Product Properties

For square matrices $A$ and $B$ of order 2, select all statements that are always true from . (Here, $E$ is the identity matrix and $O$ is the zero matrix.) [3 points]
ㄱ. $( A + B ) ^ { 2 } = A ^ { 2 } + 2 A B + B ^ { 2 }$ ㄴ. If $A ^ { 2 } + A - 2 E = O$, then $A$ has an inverse matrix. ㄷ. If $A \neq O$ and $A ^ { 2 } = A$, then $A = E$.
(1) ㄱ
(2) ㄴ
(3) ㄷ
(4) ㄱ, ㄴ
(5) ㄴ, ㄷ

For square matrices $A$ and $B$ of order 2, select all statements that are always true from <Remarks>. (Here, $E$ is the identity matrix and $O$ is the zero matrix.) [3 points]

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

Paper Questions

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