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please solve rd sharma class 12 chapter adjoint and inverse of a matrix exercise multiple choice questions question 7 maths textbook solution

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: option (c) a6

Given: A=\left[\begin{array}{lll} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{array}\right]

Hint: Find  \left | adj A \right | , find adj A

Solution:

\begin{aligned} &A=\left[\begin{array}{lll} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{array}\right]\\ &\operatorname{Adj} A=\left[\begin{array}{ccc} a^{2} & 0 & 0 \\ 0 & a^{2} & 0 \\ 0 & 0 & a^{2} \end{array}\right]^{T}\\ &=\left[\begin{array}{ccc} a^{2} & 0 & 0 \\ 0 & a^{2} & 0 \\ 0 & 0 & a^{2} \end{array}\right]\\ &|\operatorname{adjA}|=a^{2}\left(a^{4}-0\right)=a^{2} \cdot a^{4}=a^{6} \end{aligned}

Hence, option c is correct.

 

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