Question

(10 points) Are the following statements true or false? True 1. For square matrices A and B, if AB is invertible, then B is invertible. True 2. If A is a square matrix satisfying A^3 = I, then A is invertible. False 3. If all the diagonal entries of a square matrix are zero, the matrix is not invertible. True 4. If A is a square matrix satisfying A^2 = O (where O is the zero matrix), then A + I is invertible. False 5. There exists an invertible matrix A such that A^5 = O, where O is the zero matrix.

          (10 points) Are the following statements true or false?
True 1. For square matrices A and B, if AB is invertible, then B is invertible.
True 2. If A is a square matrix satisfying A^3 = I, then A is invertible.
False 3. If all the diagonal entries of a square matrix are zero, the matrix is not invertible.
True 4. If A is a square matrix satisfying A^2 = O (where O is the zero matrix), then A + I is invertible.
False 5. There exists an invertible matrix A such that A^5 = O, where O is the zero matrix.

(10 points) Are the following statements true or false?
True 1. For square matrices A and B, if AB is invertible, then B is invertible.
True 2. If A is a square matrix satisfying A^3 = I, then A is invertible.
False 3. If all the diagonal entries of a square matrix are zero, the matrix is not invertible.
True 4. If A is a square matrix satisfying A^2 = O (where O is the zero matrix), then A + I is invertible.
False 5. There exists an invertible matrix A such that A^5 = O, where O is the zero matrix.

Added by Joshua R.

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