Solution IDZ Ryabushko 1.1 - Option 10

Section: Chapter 1. Determinants. Matrices. Systems of linear algebraic equations
Topic: Determinants and matrices
Description: Calculation of determinants by expansion along a row or column, obtaining zeros. Operations with matrices: addition, multiplication, finding the inverse of a matrix.

Tasks:
1. For a given determinant Δ find minors and algebraic complements of elements aᵢ₂, a₃ⱼ. Calculate the determinant Δ: a) expanding it into elements of the i-th row; b) decomposing it into elements of the j-th column; c) having previously received zeros in the i-th row.
2. Given two matrices A and B. Find: a) AB; b) BA; c) A⁻¹; d) AA⁻¹; e) A⁻¹A

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