Question

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

• A. The product of entries in the main diagonal of $M$ is not the square of an integer
• B. The first column of $M$ is the transpose of the second row of (M\)
• C. The second row of $M$ is the transpose of the first column of $M$
• D. $M$ is a diagonal matrix with nonzero entries in the main diagonal

Answer 1

Answer: (A), (D)

$M$ is a diagonal matrix with nonzero entries in the main diagonal

Let $M=\left[\begin{array}{cc}a& b\\ b& c\end{array}\right]$, where $a,b,c,\in l$ for invertible matrix, $det\left(M\right)\ne 0\Rightarrow ac-b^2\ne 0$
i.e. $ac\ne b^2$
So, options (3) $\&$ (4) satisfies the above condition.