What is the area of the triangle with vertices $(4, 4)$,$(3, -2)$,and $(3, -16)$?

If ${a^2} + {b^2} + {c^2} + ab + bc + ca \leq 0$ for all $a, b, c \in R$,then find the value of the determinant $\left| {\begin{array}{*{20}{c}} {{(a + b + c)}^2} & {{a^2} + {b^2}} & 1 \\ 1 & {{(b + c + 2)}^2} & {{b^2} + {c^2}} \\ {{c^2} + {a^2}} & 1 & {{(c + a + 2)}^2} \end{array}} \right|$.

If $A_{\lambda} = \begin{bmatrix} \lambda & \lambda - 1 \\ \lambda - 1 & \lambda \end{bmatrix}; \lambda \in N$,then $|A_1| + |A_2| + \dots + |A_{300}|$ is equal to

Evaluate the determinant: $\left|\begin{array}{ccc}0 & 1 & 2 \\ -1 & 0 & -3 \\ -2 & 3 & 0\end{array}\right|$

If the area of the triangle with vertices $(x, 0), (1, 1)$ and $(0, 2)$ is $4$ square units,then a value of $x$ is

If $A \neq O$ and $B \neq O$ are $n \times n$ matrices such that $AB = O$,then