$$\left| {\matrix{ {a - b} & {b - c} & {c - a} \cr {b - c} & {c - a} & {a - b} \cr {c - a} & {a - b} & {b - c} \cr } } \right| = $$

Let A and B are orthogonal matrices and det A + det B = 0. Then

Let $$A = \left( {\matrix{ 2 & 0 & 3 \cr 4 & 7 & {11} \cr 5 & 4 & 8 \cr } } \right)$$. Then

If the matrix M_r is given by $${M_r} = \left( {\matrix{ r & {r - 1} \cr {r - 1} & r \cr } } \right)$$ for r = 1, 2, 3, ... then det (M₁) + det (M₂) + ... + det (M₂₀₀₈) =