taiwan-gsat 2023 Q11

taiwan-gsat · Other · gsat__math-a 5 marks Matrices True/False or Multiple-Select Conceptual Reasoning

On the coordinate plane, let $A$ and $B$ denote the rotation matrices for clockwise and counterclockwise rotation by $90^{\circ}$ about the origin respectively. Let $C$ and $D$ denote the reflection matrices with reflection axes $x = y$ and $x = -y$ respectively. Select the correct options.
(1) $A$ and $C$ map the point $(1,0)$ to the same point
(2) $A = -B$
(3) $C = D^{-1}$
(4) $AB = CD$
(5) $AC = BD$

On the coordinate plane, let $A$ and $B$ denote the rotation matrices for clockwise and counterclockwise rotation by $90^{\circ}$ about the origin respectively. Let $C$ and $D$ denote the reflection matrices with reflection axes $x = y$ and $x = -y$ respectively. Select the correct options.\\
(1) $A$ and $C$ map the point $(1,0)$ to the same point\\
(2) $A = -B$\\
(3) $C = D^{-1}$\\
(4) $AB = CD$\\
(5) $AC = BD$

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