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Question: If A is non-singular matrix, then Det \(\left( A^{- 1} \right) =\)...

If A is non-singular matrix, then Det (A−1)=\left( A^{- 1} \right) =

A

Det(1A2)\left( \frac{1}{A^{2}}^{} \right)

B

1Det(A2)\frac{1}{\text{Det}\left( A^{2} \right)}

C

Det(1A)\text{Det}\left( \frac{1}{A} \right)

D

1Det(A)\frac{1}{\text{Det}(A)}

Answer

1Det(A)\frac{1}{\text{Det}(A)}

Explanation

Solution

det

(AA−1)=det⁡(I)⇒det⁡(A)det⁡(A−1)=1⇒det⁡(A−1)=1det⁡(A)\left( AA^{- 1} \right) = \det(I) \Rightarrow \det(A)\det\left( A^{- 1} \right) = 1 \Rightarrow \det\left( A^{- 1} \right) = \frac{1}{\det(A)}