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`.

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

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

Let A and B be matrices of order n. Prove that if (I - AB) is invertible, (I - BA) is also invertible and (I-BA)^(-1) = I + B (I- AB)^(-1)A, where I be the identity matrix of order n.

Suppose A and B be two ono-singular matrices such that AB= BA^(m), B^(n) = I and A^(p) = I , where I is an identity matrix. If m = 2 and n = 5 then p equals to

Suppose A and B be two ono-singular matrices such that AB= BA^(m), B^(n) = I and A^(p) = I , where I is an identity matrix. The relation between m, n and p, is

If A^(n) = 0 , then evaluate (i) I+A+A^(2)+A^(3)+…+A^(n-1) (ii) I-A + A^(2) - A^(3) +... + (-1) ^(n-1) for odd 'n' where I is the identity matrix having the same order of A.

Suppose A and B be two ono-singular matrices such that AB= BA^(m), B^(n) = I and A^(p) = I , where I is an identity matrix. Which of the following orderd triplet (m, n, p) is false?

If A= {:[(1,2),(0,1)]:} then A^(n) is

Show that N=(N_(0))/(2^(n)) where n = number of half lives n=t/T