# Let A be a 5 by 7 , B be a 7 by 6 and C be a 6 by 5 matrix. How to determine the size of the following matrices ? AB, BA, A^TB, BC, ABC , CA ,B^TA , BC^T

##### 1 Answer

According to the theory of matrix multiplication, the matrix multiplication is only defined if B has the same number of columns as rows in A, that is, if

If it is defined, as above, then the matrix AB will have m rows and p columns, ie

Furthermore, the transpose of a matrix is when rows become columns and columns become rows.

Hence, if

So in this particular question we have

Since matrix multiplication is assosciative,