← MATH 01210 · Linear Algebra
MATH 01210 · Systems & matrices
Matrix operations
Definition
Add/subtract entrywise; scalar multiply; multiply AB when columns of A = rows of B. AB ≠ BA in general. Identity I satisfies AI=IA=A.
Read this
View AB as A acting on columns of B (linear transformation composition).
(AB)ᵀ=BᵀAᵀ. Trace and determinant have special properties under products.
Powers Aⁿ make sense for square matrices.
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Try this
Attempt each problem first, then open the worked solution.
1.Compute a 2×2 product and show a pair where AB≠BA.