જો A = left( {begin{array}{*{20}{c}}3&20&1end{array}} right), તો {({A^{

Q: જો $A = \left( {\begin{array}{*{20}{c}}3&2\\0&1\end{array}} \right)$, તો ${({A^{ - 1}})^3} =\ . . .......$

$|A| = 3,\,\text{Adj}\ A = \left( {\begin{array}{*{20}{c}}1&{ - 2}\\0&3\end{array}} \right);$ $\therefore {A^{ - 1}} = \frac{1}{3}\,\left( {\begin{array}{*{20}{c}}1&{ - 2}\\0&3\end{array}} \right)$ $ \Rightarrow {({A^{ - 1}})^3} = \frac{1}{{27}}\,{\left( {\begin{array}{*{20}{c}}1&{ - 2}\\0&3\end{array}} \right)^3} $ $= \frac{1}{{27}}\,\left( {\begin{array}{*{20}{c}}1&{ - 26}\\0&{27}\end{array}} \right)$.

MCQ

ગુજરાતી માધ્યમ

જો $A = \left( {\begin{array}{*{20}{c}}3&2\\0&1\end{array}} \right)$, તો ${({A^{ - 1}})^3} =\ . . .......$

A$\frac{1}{{27}}\left( {\begin{array}{*{20}{c}}1&{ - 26}\\0&{27}\end{array}} \right)$
B$\frac{1}{{27}}\left( {\begin{array}{*{20}{c}}{ - 1}&{26}\\0&{27}\end{array}} \right)$
C$\frac{1}{{27}}\left( {\begin{array}{*{20}{c}}1&{ - 26}\\0&{ - 27}\end{array}} \right)$
D$\frac{1}{{27}}\left( {\begin{array}{*{20}{c}}{ - 1}&{ - 26}\\0&{ - 27}\end{array}} \right)$

Medium

ધોરણ 12 સાયન્સ
ગણિત
3 and 4 . determinant and metrices
JEE

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