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Let A and B two square matrices such that(A^2)B =BA. If (AB)^10 =(A^k)(B^10), then k is equal to ?

Let A and B two square matrices such that(A^2)B =BA. If (AB)^10 =(A^k)(B^10), then k is equal to ?

Grade:12

1 Answers

Sudhir Jain
11 Points
6 years ago
for (AB)ABAB= AA2BB=A3B2
Similarly (AB)3=A7B3
(AB)4=A15B4
 
Now (AB)10=A1023B10 
 
 
Solution by :-  
Mr. Sudhir Jainam
 

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