Multiplying [2 3; -1 4] × [1 -2; 3 1]

Algebra 2 · Axiom Academy

Multiply two 2 ×︎ 2 matrices by taking the dot product of each row with each column. Nice work! You've multiplied two 2 ×︎ 2 matrices by hand. Remember these key points: Dot product pattern: each entry of the product is the dot product of a row from the first matrix with a column from the second. Position matters: entry (i,j) of the product comes from row i of the first matrix and column j of the second. Order matters: matrix multiplication is not commutative in general — for most matrices. Systematic approach: work through each entry in order — (1,1) , (1,2) , (2,1) , (2,2) — so nothing gets skipped. This method extends to any size: an matrix times an matrix always gives an result, computed the same row-by-column way.

This is the written version of the interactive lesson above. See the full Algebra 2 course.