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Since the multiplication between two matrices is not <em>commutative</em>, then , regardless of the dimensions of
.
<h3>Is the product of two matrices commutative?</h3>
In linear algebra, we define the product of two matrices as follows:
, where
,
and
(1)
Where each element of the matrix is equal to the following dot product:
, where 1 ≤ i ≤ m and 1 ≤ j ≤ n. (2)
Because of (2), we can infer that the product of two matrices, no matter what dimensions each matrix may have, is not <em>commutative</em> because of the nature and characteristics of the definition itself, which implies operating on a row of the <em>former</em> matrix and a column of the <em>latter</em> matrix.
Such <em>"arbitrariness"</em> means that <em>resulting</em> value for will be different if the order between
and
is changed and even the dimensions of
may be different. Therefore, the proposition is false.
To learn more on matrices: brainly.com/question/9967572
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