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Matrix multiplication and Composition

In order to describe the effects of multiple sequential matrix transformation, such as a rotate and then a shear, we use matrix multiplication on those individual matrices to create a new matrix, called composition, to perform the action at once. 

IBQmm-matrix-rotation-then-shear.gif

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MM_matrix-multiplication-example.gif

Matrix Multiplication is Associative

Also this is associative, meaning that parentheses does not matter, the pattern will still have the same result as long as the right to left order is the same 

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MM_matrix-shear-then-rotate.gif

MM_matrix-rotate-then-shear.gif

Also this is associative, meaning that parentheses does not matter, the pattern will still have the same result as long as the right to left order is the same 

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MM_matrix-abc-associative.gif

MM_matrix-associative.gif

End result will always look the same 

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