The inverse matrix of $A = \left[ {\begin{array}{*{20}{c}} {0\;\;1\;\;2}\\ {1\;\;\,2\;\;3}\\ {3\;\;1\;\;1} \end{array}} \right]$ is

$\left[ {\begin{array}{*{20}{c}} {\frac{1}{2}}&{ - \frac{1}{2}}&{\frac{1}{2}}\\ { - 4}&3&{ - 1}\\ {\frac{5}{2}}&{ - \frac{3}{2}}&{\frac{1}{2}} \end{array}} \right]$

$\left[ {\begin{array}{*{20}{c}} {\frac{1}{2}}&{ - 4}&{\frac{5}{2}}\\ 1&{ - 6}&3\\ 1&2&{ - 1} \end{array}} \right]$

$\frac{1}{2}\left[ {\begin{array}{*{20}{c}} 1&2&3\\ 3&2&1\\ 4&2&3 \end{array}} \right]$

$\frac{1}{2}\left[ {\begin{array}{*{20}{c}} 1&{ - 1}&{ - 1}\\ { - 8}&6&{ - 2}\\ 5&{ - 3}&1 \end{array}} \right]$

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JEE MATHEMATICS MCQ: MATRICES

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The inverse matrix of

A = \left[ {\begin{array}{cccccccccccccccccccc} {0\;\;1\;\;2}\\ {1\;\;\,2\;\;3}\\ {3\;\;1\;\;1} \end{array}} \right]

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Correct option: A

\left[ {\begin{array}{cccccccccccccccccccc} {\frac{1}{2}}&{ - \frac{1}{2}}&{\frac{1}{2}}\\ { - 4}&3&{ - 1}\\ {\frac{5}{2}}&{ - \frac{3}{2}}&{\frac{1}{2}} \end{array}} \right]

The correct answer is A. The inverse of a matrix is found by dividing the adjoint by the determinant. After calculating the determinant and adjoint, the inverse is found to be option A.

JEE MATHEMATICS MCQ: MATRICES

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