Can you invert me 2

What this matrix decomposition interview question tests

This is a medium-difficulty question on eigenvalue decomposition and determinant properties, common in quant interviews for roles in risk modelling, portfolio optimization, and statistical computing. It gauges whether you understand how determinants behave under orthogonal transformations and can simplify matrix expressions without getting lost in notation.

To solve problems like this, you need to recall how determinants compose under matrix multiplication, and specifically what happens when one of the factors is an orthogonal matrix. The key is recognizing which properties of orthogonal matrices (and their transposes) simplify the determinant calculation. Interviewers are testing whether you can move fluidly between the formal definition and practical reasoning about matrix structure.

• Multiplicativity of determinants: det(AB) = det(A)det(B)
• Properties of orthogonal matrices and their determinants
• Relationship between eigenvalues and determinants