ISRO 2013 - matrices [Mech]

Question

If A=$\begin{bmatrix} 8 & 5 & \\ 7& 6 & \end{bmatrix}$ then  |$A^{121}$ - $A^{120}$ | is:

a) 0

b) 1

c) 120

d) 121

Comments

$| A^{121} - A^{120} = |A^{120} (A - I) |$ and $|A - I| = 0$

Hence, (A) option

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|A ¹²¹ - A ¹²⁰ | = A ^ 120(A-I)

when U find A-I , U will get  0. 

thats why A) 0 will be answer

Answer 1

Ans is 0 take A^120 common

A-I have similar row so

|A-I|=0