Determinant of $3 \times 3$ Matrix problems and solutions

In matrices, evaluating the determinants of $3 \times 3$ square matrix are one type of problems. The determinant of a square matrix of order $3$ can be calculated by either formula or simplifying. The following questions are the list of determinant problems with solutions to learn how to find the determinant of any $3 \times 3$ matrix in mathematics.

Evaluate ${\begin{vmatrix} a^2+2a & 2a+1 & 1 \\ 2a+1 & a+2 & 1 \\ 3 & 3 & 1 \\ \end{vmatrix}}$

Find ${\begin{vmatrix} 1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2 \\ \end{vmatrix}}$