Three points $A(1,0), B(0,1), C(-1,0)$ are given on the coordinate plane. Let $\Gamma$ be the graph obtained by transforming $\triangle ABC$ by the matrix $T = \left[\begin{array}{ll} 3 & 0 \\ a & 1 \end{array}\right]$, where $a$ is a real number. Select the correct options. (1) If $a = 0$, then $\Gamma$ is an isosceles right triangle (2) At least two points on the sides of $\triangle ABC$ have unchanged coordinates after transformation by $T$ (3) $\Gamma$ must have part of it in the fourth quadrant (4) There exists a figure $\Omega$ on the plane such that after transformation by $T$ it becomes $\triangle ABC$ (5) The area of $\Gamma$ is a constant value
Three points $A(1,0), B(0,1), C(-1,0)$ are given on the coordinate plane. Let $\Gamma$ be the graph obtained by transforming $\triangle ABC$ by the matrix $T = \left[\begin{array}{ll} 3 & 0 \\ a & 1 \end{array}\right]$, where $a$ is a real number. Select the correct options.\\
(1) If $a = 0$, then $\Gamma$ is an isosceles right triangle\\
(2) At least two points on the sides of $\triangle ABC$ have unchanged coordinates after transformation by $T$\\
(3) $\Gamma$ must have part of it in the fourth quadrant\\
(4) There exists a figure $\Omega$ on the plane such that after transformation by $T$ it becomes $\triangle ABC$\\
(5) The area of $\Gamma$ is a constant value