DeterminantHard
Question
Suppose A is a matrix such that A2 = A and (I + A)10 = I + kA, then k is
Options
A.127
B.511
C.1023
D.1024
Solution
A2 = A
⇒ A-1 A2 = A-1A ⇒ A = I
∴ (I + A)10 = (I + I)10 = (2I)10
= 1024 I = I + KI = (K + 1) I
∴ K + 1 = 1024 ⇒ K = 1023
⇒ A-1 A2 = A-1A ⇒ A = I
∴ (I + A)10 = (I + I)10 = (2I)10
= 1024 I = I + KI = (K + 1) I
∴ K + 1 = 1024 ⇒ K = 1023
Create a free account to view solution
View Solution FreeMore Determinant Questions
If ᐃ1 = , ᐃ2 = , then the value of ᐃ1 - ᐃ2 is...Given that q2 - pr < 0, p > 0, then the value of is -...The number of different possible orders of matrices having 12 identical elements is...Matrix A is such that A2 = 2A - I, where I is the identity matrix. Then for n ≥ 2, An =...If f(x) = log10x and g(x) = eipx and h(x) = , then the value of h(10) is...