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Using properties of determinants, prove that

|(a + x, y, z), (x, a + y, z), (x, y, a + z)| = a2(a + x + y + z) = RHS

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Applying C1 → C1 + C2 + C3, we get

Expanding along R1, we get 

= (a + x + y + z) {0 + a (a + z – z)} = a2(a + x + y + z) = RHS

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