We know that , (AB)^ 1=1AB ⇒ (AB)(AB)^ 1=(AB)×1(AB) ⇒ (AB)(AB)^ 1=1=R.H.S ⇒ L.H.S=R.H.S Hence proved ...

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Implicit Differentiation

Prove that ...

Question

Prove that $(A B) (A B)^{- 1} = 1$

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Solution

We know that ,

$(A B)^{- 1} = \frac{1}{A B}$

$\Rightarrow (A B) (A B)^{- 1} = (A B) \times \frac{1}{(A B)}$

$\Rightarrow (A B) (A B)^{- 1} = 1 = R . H . S$

$\Rightarrow L . H . S = R . H . S$

Hence proved

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