GATE 2024 PI – Question 36
Engineering Mathematics · Linear Algebra · 2 marks · Multiple choice
$$A=\begin{pmatrix}a&b\\c&-a\end{pmatrix}.$$ If A² = I, which equation is true?
- $1+a^2+bc=0$
- $1-a^2+bc=0$
- $1-a^2-bc=0$
- $1+a^2-bc=0$
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Show answer and explanation
Correct answer: (C) $1-a^2-bc=0$
Explanation
Direct multiplication gives $A^2=(a^2+bc)I$, as the off-diagonal terms cancel. Thus $a^2+bc=1$, or **1−a²−bc = 0, C**.
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