Step 2: Write down the formula for the determinant of a 3x3 matrix: Det(J) = a(ei - fh) - b(di - fg) + c(dh - eg), where J = [[a, b, c], [d, e, f], [g, h, i]].
Step 3: Assign values from the matrix to the variables: a = 1, b = 2, c = 1, d = 0, e = 1, f = 2, g = 1, h = 0, i = 1.
Step 4: Calculate the first part: ei - fh = (1*1) - (2*0) = 1 - 0 = 1.
Step 5: Calculate the second part: di - fg = (0*1) - (2*1) = 0 - 2 = -2.
Step 6: Calculate the third part: dh - eg = (0*0) - (1*1) = 0 - 1 = -1.
Step 7: Substitute these values back into the determinant formula: Det(J) = 1(1) - 2(-2) + 1(-1).
