If Bn-A=I and A=[26&26&18 25&37&17 52&39&50], B=[1&4&2 3&5&1 7&1&6], then n =

Question

If Bn-A=I and A=[26&26&18 25&37&17 52&39&50], B=[1&4&2 3&5&1 7&1&6], then n = (A) 2 (B) 3 (C) 4 (D) 5

Tardigrade Admin · Accepted Answer

∵ Bn-A=I ∴ Bn=I+A Bn=[1&0&0 0&1&0 0&0&1]+[26&26&18 25&37&17 52&39&50] Bn=[27&26&18 25&38&17 52&39&51] or [1&4&2 3&5&1 7&1&6]n=[27&26&18 25&38&17 52&39&51] ...(i) ∴ n ≠1 Now put n = 2, then B2=[1&4&2 3&5&1 7&1&6]2=[1&4&2 3&5&1 7&1&6][1&4&2 3&5&1 7&1&6] =[1+12+14&4+20+2&2+4+12 3+15+7&12+25+1&6+5+6 7+3+42&28+5+6&14+1+36] =[27&26&18 25&38&17 52&39&51] Which is equal to R.H.S. of eq. (i). ∴ n=2

Q. If $B^{n} - A = I$ and $A = ⎣ ⎡ 262552263739181750 ⎦ ⎤, B = ⎣ ⎡ 137451216 ⎦ ⎤,$ then $n =$

$2$

$3$

$4$

$5$

Q. If Bn−A=I and A=⎣⎡​262552​263739​181750​⎦⎤​,B=⎣⎡​137​451​216​⎦⎤​, then n=

2

3

4

5

Q. If $B^{n} - A = I$ and $A = ⎣ ⎡ 262552263739181750 ⎦ ⎤, B = ⎣ ⎡ 137451216 ⎦ ⎤,$ then $n =$

$2$

$3$

$4$

$5$