To solve this problem, we need to identify the homoleptic complex from the given options.$\newline$A homoleptic complex is a coordination compound where all the ligands are identical.$\newline$Let's analyze each option:$\newline$• Option 1: Potassium trioxalatoaluminate (III)$\newline$ - The complex is $K_3[Al(C_2O_4)_3]. \newline$ - Here, all ligands are oxalate ions $(C_2O_4^{2-}),$ making it a homoleptic complex.$\newline$• Option 2: Diamminechloridonitrito-N-platinum (I)$\newline$ - The complex is $[Pt(NH_3)_2(Cl)(NO_2)]. \newline$ - It contains different ligands: ammine $(NH_3),$ chloride $(Cl^-),$ and nitrito $(NO_2^-). \newline$ - This is not a homoleptic complex.$\newline$• Option 3: Pentaamminecarbonatocobalt (III) chloride$\newline$ - The complex is $[Co(NH_3)_5(CO_3)]Cl_2. \newline$ - It contains ammine $(NH_3)$ and carbonate $(CO_3^{2-})$ ligands.$\newline$ - This is not a homoleptic complex.$\newline$• Option 4: Triamminetriaquachromium (III) chloride$\newline$ - The complex is $[Cr(NH_3)_3(H_2O)_3]Cl_3. \newline$ - It contains ammine $(NH_3)$ and aqua $(H_2O)$ ligands.$\newline$ - This is not a homoleptic complex.$\newline$Therefore, the correct option is Option 1: Potassium trioxalatoaluminate (III), as it is the only homoleptic complex.