If there are two values of '$$a$$' which makes determinant

$$\Delta=\left|\begin{array}{ccc} 1 & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2 a \end{array}\right|=86$$

Then, the sum of these number is

If $$A_n=\left[\begin{array}{cc}1-n & n \\ n & 1-n\end{array}\right]$$, then $$\left|A_1\right|+\left|A_2\right|+\ldots .\left|A_{2021}\right|=$$

If $$A=\left[\begin{array}{ccc}1 & -2 & 1 \\ 2 & 1 & 3\end{array}\right]$$

$$ B=\left[\begin{array}{ll}2 & 1 \\ 3 & 2 \\ 1 & 1\end{array}\right]$$, then $$(A B)^{\prime}$$ is equal to

Let $$M$$ be $$2 \times 2$$ symmetric matrix with integer entries, then $$M$$ is invertible if