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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 $A to the power of negative 1 end exponent$
$A A to the power of negative 1 end exponent equals I space equals vertical line A A to the power of negative 1 end exponent vertical line space equals space vertical line I vertical line space space equals ∣ A vertical line space vertical line A to the power of negative 1 end exponent ∣ equals 1 space equals vertical line A to the power of negative 1 end exponent space vertical line equals fraction numerator 1 over denominator vertical line A vertical line end fraction vertical line A to the power of negative 1 end exponent vertical line space equals space vertical line A vertical line to the power of negative 1 end exponent$

Therefore the correct option is choice 2

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