csat-suneung 2008 Q15

csat-suneung · South-Korea · csat__math-humanities 4 marks Matrices True/False or Multiple-Select Conceptual Reasoning

For two non-zero real numbers $a , b$, two square matrices $A , B$ satisfy $AB = \left( \begin{array} { l l } a & 0 \\ 0 & b \end{array} \right)$. Which of the following in are correct? [4 points]
ㄱ. If $a = b$, then the inverse matrix $A ^ { - 1 }$ of $A$ exists. ㄴ. If $a = b$, then $A B = B A$. ㄷ. If $a \neq b$ and $A = \left( \begin{array} { l l } 1 & 0 \\ 1 & 1 \end{array} \right)$, then $A B = B A$.
(1) ㄱ
(2) ㄷ
(3) ㄱ, ㄴ
(4) ㄴ, ㄷ
(5) ㄱ, ㄴ, ㄷ

For two non-zero real numbers $a , b$, two square matrices $A , B$ satisfy $AB = \left( \begin{array} { l l } a & 0 \\ 0 & b \end{array} \right)$. Which of the following in <Remarks> are correct? [4 points]

<Remarks>\\
ㄱ. If $a = b$, then the inverse matrix $A ^ { - 1 }$ of $A$ exists.\\
ㄴ. If $a = b$, then $A B = B A$.\\
ㄷ. If $a \neq b$ and $A = \left( \begin{array} { l l } 1 & 0 \\ 1 & 1 \end{array} \right)$, then $A B = B A$.\\
(1) ㄱ\\
(2) ㄷ\\
(3) ㄱ, ㄴ\\
(4) ㄴ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ

Paper Questions

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