First slide

Operations of matrix

Question

${Let A and B be two non-singular square matrices such that B≠I and AB}^{2} = B A . I f A^{3} = B^{- 1} A^{3} B^{n}, t h e n t h e v a l u e o f n i s$

Easy

Solution

${BA=AB}^{2} A^{- 1} (B A) = B^{2} (A^{- 1} {B A)}^{m} = B^{2 m} A^{- 1} B^{m} A = B^{2 m} B^{m} A = A B^{2 m} a l s o, B A = A B^{2} A = B^{- 1} A B^{2} A^{n} = B^{- 1} A^{n} B^{2 n}$

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