Provide an Appropriate Response $P$ Be A $5 \times 5$ Matrix That Has a Multiplicative Inverse

Multiple Choice

Provide an appropriate response.
-Let $P$ be a $5 \times 5$ matrix that has a multiplicative inverse. Which of the following statements are false? (Let 0 represent the $5 \times 5$ zero matrix.)
(i) $0 \cdot \mathrm { P } = 0$
(ii) $\mathrm { PP } ^ { - 1 } = 0$
(iii) $\mathrm { P } ^ { - 1 } \mathrm { P } = \mathrm { I } _ { 5 }$
(iv) $\mathrm { PP } ^ { - 1 } = \mathrm { P }$

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