Find the determinant of A = [[1, 2, 3], [0, 4, 5], [0, 0, 6]].

Step 1: Identify the structure of the matrix.

A = [[1, 2, 3], [0, 4, 5], [0, 0, 6]]

This is an upper triangular matrix because all entries below the main diagonal are zero.

Step 2: Recall the determinant rule for triangular matrices.

The determinant of a triangular matrix is the product of its diagonal entries.

The diagonal entries are 1, 4, and 6.

Step 3: Multiply the diagonal entries.

det(A) = (1)(4)(6)

det(A) = 24

Therefore, the determinant of A is 24.