jee-main 2023 Q74

jee-main · India · session1_29jan_shift1 3x3 Matrices Matrix Algebraic Properties and Abstract Reasoning

Let $\alpha$ and $\beta$ be real numbers. Consider a $3 \times 3$ matrix $A$ such that $A ^ { 2 } = 3 A + \alpha I$. If $A ^ { 4 } = 21 A + \beta I$, then
(1) $\alpha = 1$
(2) $\alpha = 4$
(3) $\beta = 8$
(4) $\beta = - 8$

Let $\alpha$ and $\beta$ be real numbers. Consider a $3 \times 3$ matrix $A$ such that $A ^ { 2 } = 3 A + \alpha I$. If $A ^ { 4 } = 21 A + \beta I$, then\\
(1) $\alpha = 1$\\
(2) $\alpha = 4$\\
(3) $\beta = 8$\\
(4) $\beta = - 8$

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