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Question Number 107331 by saorey0202 last updated on 10/Aug/20

$$\mathrm{If}A\mathrm{is}\mathrm{an}\mathrm{invertible}\mathrm{matrix},\mathrm{then}\det \left(A^{-1}\right)$$$$\mathrm{is}\mathrm{equal}\mathrm{to}$$

Answered by udaythool last updated on 10/Aug/20

$${AA}^{-1}=I$$$$\Rightarrow \mid {AA}^{-1}\mid =\mid A\mid \cdot \mid A^{-1}\mid =\mid I\mid =1$$$$\Rightarrow \mid A^{-1}\mid =\frac{1}{\mid A\mid }$$

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