GATE Computer Science (CS) 2020 Solved Papers

Let A and B be two n × n matrices over real numbers. Let rank(M) and det(M) denote the rank and determinant of a matrix M, respectively. Consider the following statements.
I. $\mathrm{rank}\left(\mathit{A}\mathit{B}\right)=\mathit{r}\mathit{a}\mathit{n}\mathit{k}\left(\mathit{A}\right)\mathit{r}\mathit{a}\mathit{n}\mathit{k}\left(\mathit{B}\right)$
II. $\det \left(\mathit{A}\mathit{B}\right)=\mathit{d}\mathit{e}\mathit{t}\left(\mathit{A}\right)\mathit{d}\mathit{e}\mathit{t}\left(\mathit{B}\right)$
III. $\mathrm{rank}\left(\mathit{A}+\mathit{B}\right)\le \mathit{r}\mathit{a}\mathit{n}\mathit{k}\left(\mathit{A}\right)+\mathit{r}\mathit{a}\mathit{n}\mathit{k}\left(\mathit{B}\right)$
IV. $\det \left(\mathit{A}+\mathit{B}\right)\le \mathit{d}\mathit{e}\mathit{t}\left(\mathit{A}\right)+\mathit{d}\mathit{e}\mathit{t}\left(\mathit{B}\right)$
Which of the above statements are TRUE?