3 and 4 .Determinants and Matrices
easy

यदि $A = \left( {\begin{array}{*{20}{c}}2&{ - 1}\\{ - 1}&2\end{array}} \right)$ और $I$, कोटि $2$ का इकाईआव्यूह हो, तो ${A^2}$ का मान होगा

A

$4A - 3I$

B

$3A - AI$

C

$A - I$

D

$A + I$

Solution

(a)${A^2} = A\,.\,A = \left[ {\begin{array}{*{20}{c}}{\rm{2}}&{ – 1}\\{ – 1}&2\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}{\rm{2}}&{ – 1}\\{ – 1}&2\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{\rm{5}}&{ – 4}\\{ – 4}&5\end{array}} \right]$

==> $4A – 3I = \,\left[ {\begin{array}{*{20}{c}}{\rm{8}}&{ – 4}\\{ – 4}&8\end{array}} \right]\, – \,\left[ {\begin{array}{*{20}{c}}{\rm{3}}&0\\0&3\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}5&{ – 4}\\{ – 4}&5\end{array}} \right]$.

Standard 12
Mathematics

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