Answer
$a^5$
Work Step by Step
Step 1. Start from the original, expand the determinant using the first column: $\begin{array}( \\|A|=\begin{vmatrix} a&a&a&a&a\\0&a&a&a&a\\0&0&a&a&a\\0&0&0&a&a\\0&0&0&0&a \end{vmatrix}=a \\ \\ \end{array} \begin{vmatrix} a&a&a&a\\0&a&a&a\\0&0&a&a\\0&0&0&a \end{vmatrix}$
Step 2. Again, use column1 to expand and get: $\begin{array}( \\|A|=a^2 \\ \\ \end{array} \begin{vmatrix} a&a&a\\0&a&a\\0&0&a \end{vmatrix}=a^3 \begin{vmatrix} a&a\\0&a \end{vmatrix}$
Step 3. Calculate the last determinant to reach the final results $|A|=a^5$
