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Please silve r d sharma class 12 chapter 6 adjoin and inverse of matrix exercise multiple choice quesion 1 maths textbook solution

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\left | A^{-1} \right |=\left | A \right |^{-1}    

Given: A is an inverse matrix

Hint: We will try to discard the option here.

Solutions:   since, A is invertible  \Rightarrow A^{-1} exist.

By the matrix properties of invertible matrix A 

 We have, \left | A^{-1} \right |=\left | A \right |^{-1},    \left ( A^{T} \right )^{-1}=\left ( A^{-1} \right )^{T} and   A\neq 0  all are true.

Only \left ( A^{2} \right )^{-1}=\left ( A^{-1} \right )^{2} remains in option (a) which is incorrect.

Therefore, option (a) is not true.

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