Q52Section I (Objective (Q1–Q80))52 of 80

Invariance and symmetry of $XGX'$

Consider the following statements under the linear model $\mathbf Y=X\boldsymbol\beta+\boldsymbol\varepsilon$ and $G$ be a generalized inverse of $X'X$ :

I. $XGX'$ is invariant to $G$ .

II. $XGX'$ is symmetric only when $G$ is symmetric.

Which of the statements given above is/are correct?

Pick an option to check your answer. In a mock test a wrong answer here costs 0.83 mark.

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