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Key Concepts
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1. Adjoint of a Matrix
The adjoint of matrix A, denoted as adj(A), is the transpose of the matrix of cofactors of A.
2. Condition for Invertibility
A square matrix A is invertible if and only if it is non-singular, i.e., |A| ≠ 0.
3. Formula for Inverse
A⁻¹ = (1 / |A|) · adj(A)
4. Properties of Inverse
- (A⁻¹)⁻¹ = A
- (AB)⁻¹ = B⁻¹A⁻¹
- (Aᵀ)⁻¹ = (A⁻¹)ᵀ