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Matrix Multiplication

Row times column gives the numbers. One transformation followed by another gives the meaning — and explains why AB and BA are different.

Step 1 of 30

1201

0−110

????

Speed

A = [(1, 2), (0, 1)] is a shear and B = [(0, −1), (1, 0)] is a quarter turn. Each entry of AB comes from one row of A and one column of B — four entries, four row-times-column products.

A =

B =

v =

AB = \begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix}\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix} = \begin{bmatrix} ? & ? \\ ? & ? \end{bmatrix}

Read AB right to left: B acts first. Its columns are A applied to B's columns — where î and ĵ end up after both moves.

Matrix Multiplication

Row times column gives the numbers. One transformation followed by another gives the meaning — and explains why AB and BA are different.

Step 1 of 30

1201

0−110

????

Speed

A = [(1, 2), (0, 1)] is a shear and B = [(0, −1), (1, 0)] is a quarter turn. Each entry of AB comes from one row of A and one column of B — four entries, four row-times-column products.

A =

B =

v =

AB = \begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix}\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix} = \begin{bmatrix} ? & ? \\ ? & ? \end{bmatrix}

Read AB right to left: B acts first. Its columns are A applied to B's columns — where î and ĵ end up after both moves.

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Matrix Multiplication

See also

Matrix Multiplication

See also