Find the determinant of the 3x3 matrix \( A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \)

Step 1 ：The determinant of a 3x3 matrix \( A = \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} \) is given by \( det(A) = aei + bfg + cdh - ceg - bdi - afh \).

Step 2 ：Substituting the given values, we get \( det(A) = 1*5*9 + 2*6*7 + 3*4*8 - 3*5*7 - 2*4*9 - 1*6*8 \).

Step 3 ：Solving this, we get \( det(A) = 45 + 84 + 96 - 105 - 72 - 48 \).

Step 4 ：Simplifying, we get \( det(A) = 0 \).