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Find the inverse of the matrix (if it exists) given $$\left[ {\begin{array}{*{20}{c}} 2&{ - 2} \\ 4&3 \end{array}} \right]$$
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QuestionMathsClass 12

Find the inverse of the matrix (if it exists) given $$\left[ {\begin{array}{*{20}{c}} 2&{ - 2} \\ 4&3 \end{array}} \right]$$

Let $$A = \left[ {\begin{array}{*{20}{c}} 2&{ - 2} \\ 4&3 \end{array}} \right]$$
$$\therefore \left| A \right| = \left[ {\begin{array}{*{20}{c}} 2&{ - 2} \\ 4&3 \end{array}} \right] = 6 - \left( { - 8} \right) = 6 + 8 = 14 \ne 0$$
$$\therefore$$ Matrix A is non-singular and hence $${A^{ - 1}}$$ exist.
Now adj. A $$= \left[ {\begin{array}{*{20}{c}} 3&2 \\ { - 4}&2 \end{array}} \right]$$ And $${A^{ - 1}} = \frac{1}{{\left| A \right|}}adj.A = \frac{1}{{14}}\left[ {\begin{array}{*{20}{c}} 3&2 \\ { - 4}&2 \end{array}} \right]$$