Read the following definition carefully, and then answer the question below. An n  n matrix A is called weak if A is not a zero matrix, but there is some power of A which is a zero matrix, i.e. Ak is the zero matrix On for some k > 1. 3.1 Is it possible for a weak matrix A to be invertible? If so, create an example, and show that it is both weak and invertible. If not, explain why not. For which value(s) (if any) of a is the following matrix weak? ( first row : a  1  0 second row : 0 a 1 third row:      0 0 a) Hint: what happens on the main diagonal of A^k?

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