GATE Civil 2022 Set 2 | Question: 15

Question

$\text{P}$ and $\text{Q}$ are two square matrices of the same order. Which of the following statement(s) is/are correct?

• A. If $\text{P}$ and $\text{Q}$ are invertible, then $\text{[PQ]}^{-1} = \text{Q}^{-1} \text{P}^{-1}.$
• B. If $\text{P}$ and $\text{Q}$ are invertible, then $\text{[QP]}^{-1} = \text{P}^{-1} \text{Q}^{-1}.$
• C. If $\text{P}$ and $\text{Q}$ are invertible, then $\text{[PQ]}^{-1} = \text{P}^{-1} \text{Q}^{-1}.$
• D. If $\text{P}$ and $\text{Q}$ are not invertible, then $\text{[PQ]}^{-1} = \text{Q}^{-1} \text{P}^{-1}.$