Question 171320
let A be a 5 X 3 matrix and B be a 3 X 5 matrix
a) is it possible to add A and B?
<pre><font size = 4 color = "indigo"><b>
No, because in order to add them, they must have exactly 
the same dimensions.
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b) is it possible to do the multiplication AB?
<pre><font size = 4 color = "indigo"><b>
Yes because there are the same number of columns in the 
first matrix A, 5 x 3, as there are columns in B, the
3 x 5 matrix.  That is when you write their dimensions
in the order you are wanting to multiply them:

        5 x <font color = "red">3</font>  times  <font color = "red">3</font> x 5 

The inner dimensions are both the same, in this case <font color = "red">3</font>.
And their product will be a 5 x 5, the outer two
dimensions.
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c) is it possible to do the multipllication BA?
<pre><font size = 4 color = "indigo"><b>
Yes because there are the same number of columns in the 
first matrix B, 3 x 5, as there are columns in A, the
5 x 3 matrix.  That is when you write their dimensions
in the order you are wanting to multiply them:

        3 x <font color = "red">5</font>  times  <font color = "red">5</font> x 3 

the inner dimensions are both the same, in this case 5.
And their product will be a 3 x 3, the outer two 
dimensions.

Edwin</pre>