Matrix Operations Cheat Sheet
By Dr. Iris Vaughan, Mathematics Editor·Published 1 December 2025·Last reviewed 15 January 2026
Matrix addition, multiplication, determinants (2×2 and 3×3), inverse formula, and properties of special matrices — with the conditions for each operation.
Key Formulas
Addition: same dimensions
Multiplication: (m×n)(n×p)=(m×p)
det[[a,b],[c,d]]=ad−bc
Inverse: A⁻¹=(1/det A)·adj(A)
Transpose: (AB)ᵀ=BᵀAᵀ
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