Would this statement be true regarding matrices: For ANY m x n matrices A and B, A+B = B+A, or would this only be true if the matrices were of the same size?

1 Answer
Geoff K.
Apr 29, 2018

If #A# and #B# have the same dimensions #m xx n#, then matrix addition is indeed commutative.

Explanation:

Matrix addition #A+B# is only defined when #A# and #B# are conformal. For addition, that means they must have the same number of rows and columns as each other.

Matrix addition is performed by adding corresponding elements of #A# and #B# to get the new elements of #A+B#. If #A# and #B# have different sizes, then there will be elements of one that don't have a partner in the other. In this case, the sum #A+B# does not exist.

If #A# and #B# have the same dimensions, then the addition #A+B# produces the same sum as #B+A#, because classic addition is also commutative. (That means #a+b=b+a#.)

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