Let mathbf A be an ntimes p matrix of rank r. Let mathbf A^- be any generalized inverse of mathbf A. Which of the statements given below is/are correct? 1. rank(mathbf Amathbf A^-)=rank(mathbf A^-mathbf A)=rank(mathbf A)=r. 2. (mathbf A^-)' is a generalized inverse of mathbf A'.

Q64Section I (Objective (Q1–Q80))63 of 79

Linear Algebra — rank and transpose properties of a g-inverse

Let $\mathbf A$ be an $n\times p$ matrix of rank $r$ . Let $\mathbf A^-$ be any generalized inverse of $\mathbf A$ . Which of the statements given below is/are correct? 1. $\mathrm{rank}(\mathbf A\mathbf A^-)=\mathrm{rank}(\mathbf A^-\mathbf A)=\mathrm{rank}(\mathbf A)=r$ . 2. $(\mathbf A^-)'$ is a generalized inverse of $\mathbf A'$ .

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