Maths-
General
Easy
Question
If A is invertible matrix, then det (A–1) equals-
- det A
- 1/det A
- 1
- None of these
The correct answer is: 1/det A
We are given that A is invertible matrix and asked to find det ![A to the power of negative 1 end exponent](data:image/png;base64,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)
![A A to the power of negative 1 end exponent equals I space
equals vertical line A A to the power of negative 1 end exponent vertical line space equals space vertical line I vertical line space space
equals ∣ A vertical line space vertical line A to the power of negative 1 end exponent ∣ equals 1 space
equals vertical line A to the power of negative 1 end exponent space vertical line equals fraction numerator 1 over denominator vertical line A vertical line end fraction
vertical line A to the power of negative 1 end exponent vertical line space equals space vertical line A vertical line to the power of negative 1 end exponent](data:image/png;base64,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)
Therefore the correct option is choice 2
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