# Math Help - invertable Matrix's

1. ## invertable Matrix's

1) a)Suppose that A is a square matrix of size n*n such that A^2011 = 0. Show that
the matrix A+In is invertible and find an expression for (A + In)^-1 in terms of A.
(In is a identity matrix with n*n dimensions)

b) Let A be a matrix of size 50 *49 and B a matrix of size 49* 50 matrix. Show that
the matrix AB is not invertible. Give an example of matrices A and B for which BA
is invertible

Can I get some help with there questions please? Having a hard time getting my head around them

2. a) Compute for $N\in\mathbb{N}^*$ $(A+I_n)\sum_{j=0}^N(-1)^j A^j$.