Write the Word or Phrase That Best Completes Each Statement $\mathrm { P }$

Multiple Choice

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-Let $\mathrm { P }$ be a $2 \times 2$ matrix that has a multiplicative inverse. Which of the following statements are false? (Let 0 represent the $2 \times 2$ zero matrix.)
(i) $0 \cdot \mathrm { P } = 0$
(ii) $\mathrm { PP } ^ { - 1 } = 0$
(iii) $\mathrm { P } ^ { - 1 } \mathrm { P } = \mathrm { I } _ { 2 }$
(iv) $\mathrm { PP } ^ { - 1 } = \mathrm { P }$

A) (i) , (iii)
B) (iv)
C) (ii)
D) (ii) , (iv)