QPaperGen

1. Product Rule: \(\text{det}(AB) = \text{det}(A) \cdot \text{det}(B)\)


2. Scalar Multiplication Rule: \(\text{det}(c A) = c^n \cdot \text{det}(A)\) (where \(n\) is the order of the matrix)

We take the determinant of both sides of the equation \(MN = mI\):

Since the order \(n=3\) and \(\text{det}(I) = 1\), the right side simplifies to \(\text{det}(mI) = m^3 \cdot 1 = m^3\).

Substitute \(\text{det}(M) = m\) and \(\text{det}(mI) = m^3\) we get :