taiwan-gsat 2025 Q7

taiwan-gsat · Other · ast__math-b 8 marks Matrices True/False or Multiple-Select Conceptual Reasoning

Let the second-order matrices $A = \left[ \begin{array} { l l } 1 & 0 \\ 1 & 0 \end{array} \right], B = \left[ \begin{array} { l l } 0 & 1 \\ 0 & 1 \end{array} \right]$. Select the correct options.
(1) $A ^ { 2 } = A$
(2) $A + B = B + A$
(3) $A B = B A$
(4) $( A - B ) ^ { 2 } = A ^ { 2 } - 2 A B + B ^ { 2 }$
(5) $( A + B ) ^ { 2 } = 2 ( A + B )$

Let the second-order matrices $A = \left[ \begin{array} { l l } 1 & 0 \\ 1 & 0 \end{array} \right], B = \left[ \begin{array} { l l } 0 & 1 \\ 0 & 1 \end{array} \right]$. Select the correct options.\\
(1) $A ^ { 2 } = A$\\
(2) $A + B = B + A$\\
(3) $A B = B A$\\
(4) $( A - B ) ^ { 2 } = A ^ { 2 } - 2 A B + B ^ { 2 }$\\
(5) $( A + B ) ^ { 2 } = 2 ( A + B )$

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