A square matrix A is said to be nilpotent of index m, if `A^m=0`. Now if for this A, `(I-A)^n=I+A+A^2+A^3++A^(m-1)`, then n is equal to

A square matrix A is said to be nilpotent of induare if A^(m)=0. Now if for this A,(I-A)^(n)=I+A+A^(2)+A^(3)++A^(m-1) then n is equal to

A square matrix A is said to be nilpotent of induare if A^(m)=0. Now if for this A,(I-A)^(n)=I+A+A^(2)+A^(3)++A^(m-1) then n is equal to

A square matrix B is said to be an orthogonal matrix of order n if BB^(T)=I_(n) if n^(th) order square matrix A is orthogonal, then |adj(adjA)| is

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 _______.

If A is a nilpotent matrix of index 2, then for any positive integer n,A(I+A)^(n) is equal to A^(-1) b.A c.A^(n) d.I_(n)

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

If A is a square matrix such that |A| ne 0 and m, n (ne 0) are scalars such that A^(2)+mA+nI=0 , then A^(-1)=