If $B = A B A^{- 1}$ then $A B A^{- 1}$ equals

A^{- 1} B A

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A^{- 1} B^{- 1} A

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A B A

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B^{- 1} A^{- 1}

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Solution

The correct option is D $A^{- 1} B A$
Given, $B = A B A^{- 1}$
$A^{- 1} B = (A^{- 1} A) B A^{- 1}$
$\Rightarrow A^{- 1} B = B A^{- 1}$
$∴ A^{- 1} B A = B A^{- 1} A$
Hence, $A^{- 1} B A = B = A B A^{- 1}$

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