Which of the following statements is not true?
(a) If A is an invertible matrix, then A^(2) is also invertible.
(b) If A is a square matrix satisfying the equation (A+I)^(2)=0, then
A is also invertible.
(c) If A is an invertible matrix satisfying the equation (A-I)^(2)=0,
then A is the identity matrix.
(d) If A is a square matrix satisfying the equation A^(n)=0 for n>=3,
then the matrix I-A is invertible.
(e) If A is an idempotent matrix with det(A)=1, then A is the
identity matrix.