Inverse of a Matrix and Its Applications — Important Questions

|A| ≠ 0

If the coefficient matrix A has non-zero determinant, the system has a unique solution given by X = A⁻¹B.

3

Minor M₁₂ is the determinant obtained by deleting row 1 and column 2, which leaves element 3. So M₁₂ = 3.

3

C₁₁ = (-1)¹⁺¹ × M₁₁ = 1 × |3| = 3.

5

For a 2×2 matrix, |Adj A| = |A|^(2-1) = |A| = 5.