Row of first matrix × column of second matrix. A(m×n) × B(n×p) = C(m×p). Not commutative: AB ≠ BA generally.
Computer graphics — Chaining transformations (rotate, scale, translate).
Machine learning — Neural network forward pass: output = W × input.
Economics — Input-output analysis: X = (I-A)⁻¹D.
Markov chains — State transitions: P^n gives n-step probabilities.
Cryptography — Hill cipher encryption.
Quantum computing — Quantum gate operations.
Signal processing — Filter banks and convolutions.
Network analysis — Path counting in graphs.
Robotics — Forward kinematics: joint angles to end effector.
Google PageRank — Web page importance via matrix powers.
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