If the multiplicative group of 2 × 2 matrices of the form ( * 20 … - Vidyadip

MCQ

If the multiplicative group of $2 × 2$ matrices of the form $\left( {\begin{array}{*{20}{c}}a&a\\a&a\end{array}} \right)$, for $a \ne 0$ and $a \in R$, then the inverse of $\left( {\begin{array}{*{20}{c}}2&2\\2&2\end{array}} \right)$ is

A
$\left( {\begin{array}{*{20}{c}}{\frac{1}{8}}&{\frac{1}{8}}\\{\frac{1}{8}}&{\frac{1}{8}}\end{array}} \right)$
B
$\left( {\begin{array}{*{20}{c}}{\frac{1}{4}}&{\frac{1}{4}}\\{\frac{1}{4}}&{\frac{1}{4}}\end{array}} \right)$
C
$\left( {\begin{array}{*{20}{c}}{\frac{1}{2}}&{\frac{1}{2}}\\{\frac{1}{2}}&{\frac{1}{2}}\end{array}} \right)$
✓
Does not exist

✓

Answer

Correct option: D.

Does not exist

d
(d) Given, $A$ multiplicative group of $2 × 2$ matrices of the form $\left( {\begin{array}{*{20}{c}}a&a\\a&a\end{array}} \right)$. Let $A = \left| {\,\begin{array}{*{20}{c}}2&2\\2&2\end{array}\,} \right|$ since $|A| = 0$, therefore inverse of $ A$ does not exist.

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