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Provide solution for rd sharma maths class 12 chapter adjoint and inverse of a matrix exercise multiple choice question question 10

Answers (1)

option (c) 10

Give: A\left ( adj A \right )=\begin{bmatrix} 10 &0 \\ 0 & 10 \end{bmatrix}

Hint: calculating determinant of A i.e; |A| 

Solution:

A\left ( adj A \right )=\begin{bmatrix} 10 &0 \\ 0 & 10 \end{bmatrix}

A (adj A) = 10 I

We know that

A^{-1}=\frac{1}{|\mathrm{~A}|}(\operatorname{adj} \mathrm{A})

Pre- multiplying by ‘A’

\begin{aligned} &A A^{-1}=\frac{A(\operatorname{adjA})}{|A|} \\ &I=\frac{A(\operatorname{adjA})}{|A|} \\ &A(\operatorname{adj} A)=|A|I \\ &\Rightarrow|A|=10 \end{aligned}

Hence option (c) is correct

 

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