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Provide solution for rd sharma maths class 12 chapter adjoint and inverse of a matrix exercise multiple choice question question 16

Answers (1)

option (d) C^{-1}BA^{-1}

Given: A, B & C are non-singular square matrices of same orders

Hint: to find the answer you must know the properties of inverse

Solution: \left (AB^{-1}C \right )^{-1}

\begin{aligned} &=C^{-1}\left(B^{-1}\right)^{-1} A^{-1} \\ &=C^{-1} B A^{-1} \\ &\Rightarrow\left(A B^{-1} C\right)^{-1}=C^{-1} B A^{-1} \end{aligned}

Hence, option (d) is correct

 

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