List of top Higher Mathematics Questions on Determinants

Prove that: \[ \left| \begin{matrix} a - b - c & 2a & 2a \\ 2b & b - c - a & 2b \\ 2c & 2c & c - a - b \end{matrix} \right| = (a + b + c)^3 \]

Solve the equation: \[ \left| \begin{matrix} x+a & x & x \\ x & x+a & x \\ x & x & x+a \end{matrix} \right| = 0 \] where \( a \neq 0 \).