Final answer:
To calculate the determinant of a matrix, you need to augment the matrix, find the products along the main diagonals and the products of the minor diagonals, and perform the final calculation by subtracting the products of the minor diagonals from the sum of the products along the main diagonals.
Step-by-step explanation:
The first step to calculate the determinant of a matrix is to augment the matrix by copying columns 1 and 2 to the right of the matrix. Then, you find the products along the main diagonals and the products of the minor diagonals. After that, you perform the final calculation by subtracting the products of the minor diagonals from the sum of the products along the main diagonals.
For example, if the main diagonals have products d1, d2, and d3, and the minor diagonals have products e1, e2, and e3, the determinant of the matrix is given by d1 + d2 + d3 - e1 - e2 - e3.
Let's say d1 = 4, d2 = 0, d3 = 3, e1 = 0, e2 = 16, and e3 = 2. The determinant would be calculated as -11: d1 + d2 + d3 - e1 - e2 - e3 = 4 + 0 + 3 - 0 - 16 - 2 = -11.