Order the steps to compute AB where A and B are 2×2 matrices.

Verify dimensions are compatible (2×2 · 2 ×2) → Compute row 1 of A against column 1 of B → entry (1,1) → Repeat for all four entries → Assemble the 2 × 2 result matrix

Physics I / Matrices and Matrix Operations

Practice question · Put in order

Order the steps to compute $AB$ where $A$ and $B$ are $2\times2$ matrices.

Repeat for all four entries
Compute row 1 of A against column 1 of B → entry (1,1)
Verify dimensions are compatible (2 $\times2$ $\cdot 2 \times2)$
Assemble the $2 \times 2$ result matrix

Hints

Each entry of the product is one row paired with one column.
The full matrix is assembled only after every entry is computed.

Show the answer

Verify dimensions are compatible (2 $\times2$ $\cdot 2 \times2)$
Compute row 1 of A against column 1 of B → entry (1,1)
Repeat for all four entries
Assemble the $2 \times 2$ result matrix

Why

Each entry of the product is one dot product; assemble all four to get the result.

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Order the steps to compute $AB$ where $A$ and $B$ are $2\times2$ matrices.