Matrices and Determinants: One-Page Formula Sheet

Matrices and Determinants — formula sheet

Formulas

• A⁻¹ = adj(A)/|A|
• |adj A| = |A|^(n−1)
• |AB| = |A||B|, (AB)⁻¹ = B⁻¹A⁻¹
• Area of triangle = ½|det[x y 1]|

Key ideas

• AB ≠ BA in general
• |kA| = kⁿ|A| for an n×n matrix
• A⁻¹ exists only if |A| ≠ 0
• System AX = B: |A| ≠ 0 gives a unique solution

Traps to avoid

• Using |kA| = k|A|
• Wrong order in (AB)ᵀ = BᵀAᵀ
• Missing the infinite-solution vs no-solution case

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