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(Solved): Which of the following statements is not true? (a) If A is an invertible matrix, then A^(2) is also ...



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.


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