Question

Let A, B and Care three non-singular square matrices of same order such that B = CA * C ^ - 1 If C * A ^ 5 * C ^ - 1 is equal to B ^ m where m in N , then m is equal to

Answer 1

Given that B = CAC^-1 & CA⁵C^-1 = B^m, m\(\in \)N

B² = (CAC^-1) (CAC^-1) = CA(C^-1C) AC^-1 = CAIAC^-1

 = C.A.A.C^-1 = CA²C^-1

B⁴ = (CA²C^-1) (CA²C^-1) = CA²(C^-1C)A²C^-1

B⁵ = (CA⁴C^-1) (CAC^-1) = CA⁴(C^-1C)AC^-1

 = CA⁵C^-1

Hence, m = 5