Matrix A such that `A^(2)=2A-I`, where I is the identity matrix, then for `n ge 2, A^(n)` is equal to

Matrix A such that A^2=2A-I ,w h e r eI is the identity matrix, the for ngeq2. A^n is equal to 2^(n-1)A-(n-1)l b. 2^(n-1)A-I c. n A-(n-1)l d. n A-I

If A = [(1,2,2),(2,1,-2),(a,2,b)] is a matrix satisfying the equation "AA"^(T) = 9I , where I is 3xx3 identity matrix, then the ordered pair (a,b) is equal to

Let A=[("tan"pi/3,"sec" (2pi)/3),(cot (2013 pi/3),cos (2012 pi))] and P be a 2 xx 2 matrix such that P P^(T)=I , where I is an identity matrix of order 2. If Q=PAP^(T) and R=[r_("ij")]_(2xx2)=P^(T) Q^(8) P , then find r_(11) .

A square matrix M of order 3 satisfies M^(2)=I-M , where I is an identity matrix of order 3. If M^(n)=5I-8M , then n is equal to _______.

Let A=[(0,1),(0,0)] , show that (aI+bA)^(n)=a^(n)I+na^(n-1)bA , where I is the identity matrix of order 2 and n in N .

A square matrix P satisfies P^(2)=I-P where I is identity matrix. If P^(n)=5I-8P , then n is

If A is an invertible matrix of order 2, then det (A^(-1)) is equal to

Let A be a squàre matrix of order 2 sụch that A^2 - 4 A+4 I=O where I is an identity matrix of order 2 . If B=A^5+4 A^4+6 A^3+4 A^2+A , then det(B) is equal to

If A= ((2,3),(-1,2)) .Show that A^(2)-4A+7I=0 whwre I is the unit matrix of order 2.