Determinants

What the exams ask here

• det = 0 find abc
• det(A + A^2 + ... + A^13)
• det(2A), det(A^n)
• |I + A| when A^2=0
• det(2AB^-1C^3B^T) for 4 x 4 matrices (Indore 2019 SA Q4)
• A^2 = 0: det((I + A)^50 - 50A) (Indore 2019 SA Q5)
• +-1 matrix with row and column sums 1 (Indore 2019 SA Q13)
• |a a^2 a^3 - 1; ...| = 0 -> abc (Indore 2020 SA Q4)
• |det(A^9 + A^6 + A^3 + A)| for a permutation matrix (Indore 2022 SA Q7)
• sign of det[a b c; b c a; c a b] (Indore 2022 Q25)
• det(A^3 - 3A^2 - 5A) = 0 (Indore 2023 Q22)
• magic-square matrix (Indore 2024 SA Q15)
• |P(0) P(1); P(0) P(2)| = 0 (Indore 2025 Q23)
• |5 adj A| = 5
• Vandermonde with a + b + c = 0 (Indore 2026 SA)