Let A be a matrix of order 3 such that `A^(2)=3A-2I` where, I is an identify matrix of order 3. If `A^(5)=alphaa+betaI`, then `alphabeta` is equal to

A square matrix A of order 3 satisfies A^(2)=I-2A , where I is an identify matrix of order 3. If A^(n)=29A-12I , then the value of n is equal to

Let a be a matrix of order 2xx2 such that A^(2)=O . (I+A)^(100) =

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 be a square matrix of order 2 such that A^(2)-4A+4I=0 , where I is an identity matrix of order 2. If B=A^(5)+4A^(4)+6A^(3)+4A^(2)+A-162I , then det(B) is equal to _________

If A is a matrix of order 3, such that A(adj A)=10I, then |adj A|=

Let A be a matrix of order 3, such that A^(T)A=I . Then find the value of det. (A^(2)-I) .

If I_(3) is identity matrix of order 3, then I_(3)^(-1)=

If I_3 is the identily matrix of order 3, then (I_3)^(-1)=