1. Finding the matrix

Suppose A is a 4X2 matrix, B is a 5X4 matrix, and C is a 2X5 matrix.
For each of the following product expressions, indicate whether the
matrix product is defined, and, if so, the dimensions of the product.
(1.5 pts.)

Defined? Dimensions
------------------------------------------
AB | |
AC | |
BA | |
BC | |
CA | |
CB | |

2. The product is defined when the width of the left factor is equal to the height of the right one. The resulting product has the height of the left factor and the width of the right one.

3. Originally Posted by racewithferrari
Suppose A is a 4X2 matrix, B is a 5X4 matrix, and C is a 2X5 matrix.
For each of the following product expressions, indicate whether the
matrix product is defined, and, if so, the dimensions of the product.
(1.5 pts.) |
For matrices $A~\&~B$ the product $A_{k,j} B_{m,n}$ exists if and only if $j=m$.
The dimension of $A\cdot B$ is $k\times n$.

4. Can you elaborate your answer in an easy way so that I can understand, because I am new to this and I don't want my teacher to think that I have cheated.

5. Originally Posted by racewithferrari
Can you elaborate your answer in an easy way so that I can understand, because I am new to this and I don't want my teacher to think that I have cheated.
Examples
If $A_{3,4}~\&~B_{4,2}$ then $A\cdot B=C_{3,2}$

BUT $B\cdot A$ does not exist because $2\ne 3$.