Consider the following statements: I. If A is an idempotent matrix, then rank (A) = Trace (A). II. Given a matrix A, there exists a matrix A^-, with the property AA^-A = A and trace (A^-A) = rank (A). Which of the statements given above is/are correct?

Q55Section I (Objective (Q1–Q80))55 of 80

Linear Algebra — idempotent matrices and generalized inverses

Consider the following statements: I. If $\mathbf{A}$ is an idempotent matrix, then rank $(\mathbf{A})$ = Trace $(\mathbf{A})$ . II. Given a matrix $\mathbf{A}$ , there exists a matrix $\mathbf{A}^-$ , with the property $\mathbf{AA^-A} = \mathbf{A}$ and trace $(\mathbf{A^-A})$ = rank $(\mathbf{A})$ . Which of the statements given above is/are correct?

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