1. What is 3 Matrix Multiplication?

Three matrix multiplication (A × B × C) is performed by first multiplying matrices A and B, then multiplying the result with matrix C. The operation is associative but not commutative.

2. How Does the Calculator Work?

The calculator uses standard matrix multiplication:

Where:

• A, B, C — Input matrices
• i, j, k — Matrix indices
• ∑ — Summation over index k

Explanation: The multiplication is performed in two steps: first A × B, then the result is multiplied by C.

3. Importance of Matrix Multiplication

Details: Matrix multiplication is fundamental in linear algebra, computer graphics, physics simulations, and machine learning. Triple products appear in many mathematical and engineering applications.

4. Using the Calculator

Tips:

• Enter each matrix with rows separated by newlines and elements by spaces
• Inner dimensions must match (columns of A = rows of B, columns of AB = rows of C)
• Example format for 2×2 matrix:
  1 2
  3 4

5. Frequently Asked Questions (FAQ)

Q1: Does the order of multiplication matter?
A: The operation is associative (A×B)×C = A×(B×C) but not commutative (A×B ≠ B×A).

Q2: What are the dimension requirements?
A: If A is m×n, B must be n×p, and C must be p×q. The result will be m×q.

Q3: Can I multiply non-square matrices?
A: Yes, as long as the inner dimensions match at each multiplication step.

Q4: What's the computational complexity?
A: For n×n matrices, it's O(n³) for each multiplication, so O(n³) total.

Q5: Are there more efficient algorithms?
A: For large matrices, algorithms like Strassen's can be used, though with different tradeoffs.