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unitary matrices, determinant

Source: 2019 South Korea USMC P4

August 13, 2020
linear algebradeterminantunitary matrixcollege contests

Problem Statement

For any n×nn\times n unitary matrices A,BA,B, prove that ∣det⁡(A+2B)∣≤3n|\det (A+2B)|\leq 3^n.
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