Let $M$ be a $2\times 2$ symmetric matrix with integer entries. Then $M$ is invertible if

Which of the following values of $\mathrm{\alpha }$ satisfy the equation $\left|\begin{array}{ccc}(1+\mathrm{\alpha }{)}^2& (1+2\mathrm{\alpha }{)}^2& (1+3\mathrm{\alpha }{)}^2\\ (2+\mathrm{\alpha }{)}^2& (2+2\mathrm{\alpha }{)}^2& (2+3\mathrm{\alpha }{)}^2\\ (3+\mathrm{\alpha }{)}^2& (3+2\mathrm{\alpha }{)}^2& (3+3\mathrm{\alpha }{)}^2\end{array}\right|=-648\mathrm{\alpha }$?

Which of the following is(are) NOT the square of a $3\times 3$ matrix with real entries?

Let $A$ be a $2\times 2$ matrix

Statement $1:$ $adj\left(adjA\right)=A$

Statement $2:$ $\left|adjA\right|=|A\mid$.