If $$A=\left[\begin{array}{cc}2 & -3 \\ -4 & 1\end{array}\right]$$, then $$\left(A^T\right)^2+(12 A)^T=$$

If $$a, b, c$$ are respectively the 5 th, 8 th, 13 th terms of an arithmetic progression, then $$\left|\begin{array}{ccc}a & 5 & 1 \\ b & 8 & 1 \\ c & 13 & 1\end{array}\right|=$$

If $$A=\left[\begin{array}{ccc}1 & 0 & 0 \\ a & -1 & 0 \\ b & c & 1\end{array}\right]$$ is such that $$A^2=I$$, then

Let $$A=\left[\begin{array}{ccc}-2 & x & 1 \\ x & 1 & 1 \\ 2 & 3 & -1\end{array}\right]$$. If the roots of the equation $$\operatorname{det} A=0$$ are $$l, m$$ then $$l^3-m^3=$$