Matrices

What the exams ask here

• A^2022 for rotation/nilpotent/upper-triangular
• A^3 = 27 B find p+q+r
• (A^-1)_{ij}
• simplify (A B^-1)^-1
• inverse of [2, -0.5; -1, x] is [1, 1; 2, 4] (Indore 2019 Q38)
• 2A - B - A(A + B)^-1 A + B(A + B)^-1 B with AB = BA (Indore 2021 Q14)
• A = [1 0; 1/2 0]: A^2022 (Indore 2022 Q26)
• A = [2 n; 4 1], A^3 = 27[4 q; p r] (Indore 2025 SA Q12)
• number of 3 x 3 matrices with entries 0 or 2
• (A - B)(A + B) = A^2 - B^2 iff AB = BA