If $A$ and $B$ are two non-singular matrices of the same order Such that$B^{r} = I$, for some positive integer$r 1$. Then $A^{- 1}B^{r - 1}A - A^{- 1}B^{- 1}A = \$

Question

If $A$ and $B$ are two non-singular matrices of the same order Such that$B^{r} = I$, for some positive integer$r > 1$. Then $A^{- 1}B^{r - 1}A - A^{- 1}B^{- 1}A = \$

Dr. Abubacker · Accepted Answer

(c)
Given $B^{r} = I \Rightarrow B^{r}B^{- 1} = IB^{- 1} \Rightarrow B^{r - 1} = B^{- 1}$
$\Rightarrow A^{- 1}B^{r - 1}A - A^{- 1}B^{- 1}A = A^{- 1}B^{- 1}A - A^{- 1}B^{- 1}A = 0$

Q. If $A$ and $B$ are two non-singular matrices of the same order Such that$B^{r} = I$, for some positive integer$r > 1$. Then $A^{- 1}B^{r - 1}A - A^{- 1}B^{- 1}A = \$

Explanation

Reviewed by Dr. Abubacker

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