jee-main 2018 Q77

jee-main · India · 15apr Matrices Matrix Algebra and Product Properties

Let $A$ be a matrix such that $A \cdot \left[ \begin{array} { l l } 1 & 2 \\ 0 & 3 \end{array} \right]$ is a scalar matrix and $| 3 A | = 108$. Then, $A ^ { 2 }$ equals :
(1) $\left[ \begin{array} { c c } 4 & 0 \\ - 32 & 36 \end{array} \right]$
(2) $\left[ \begin{array} { c c } 36 & - 32 \\ 0 & 4 \end{array} \right]$
(3) $\left[ \begin{array} { c c } 36 & 0 \\ - 32 & 4 \end{array} \right]$
(4) $\left[ \begin{array} { c c } 4 & - 32 \\ 0 & 36 \end{array} \right]$

Let $A$ be a matrix such that $A \cdot \left[ \begin{array} { l l } 1 & 2 \\ 0 & 3 \end{array} \right]$ is a scalar matrix and $| 3 A | = 108$. Then, $A ^ { 2 }$ equals :\\
(1) $\left[ \begin{array} { c c } 4 & 0 \\ - 32 & 36 \end{array} \right]$\\
(2) $\left[ \begin{array} { c c } 36 & - 32 \\ 0 & 4 \end{array} \right]$\\
(3) $\left[ \begin{array} { c c } 36 & 0 \\ - 32 & 4 \end{array} \right]$\\
(4) $\left[ \begin{array} { c c } 4 & - 32 \\ 0 & 36 \end{array} \right]$

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