Proving AB and BA are Square Matrices

[forty]

1)
Show that if matrix products AB and BA are both defines, then AB and BA are square matrices:



Let A = a m*n matrix

IF AB is defined then B must have n rows (n*?) matrix

IF BA is defined then B must have m columns making it a n*m matrix

so BA = (n*m) * (m*n) = (n*n) matrix

AB = (m*n) * (n*m) = (m*m) matrix



2)
Show that if A is an m*n matrix and A(BA) is defined, then B is an n*m matrix.



IF BA is defined and A is m*n matrix then B must be a ?*m matrix

BA produces a ?*n matrix

IF A(BA) is defined BA must be a n*n matrix

AS BA is an n*n matrix B must be a n*m matrix


Do these work as a proofs, if they even follow any logic in the first place (I'm horrid when it comes to matrices)

Any input would be greatly appreciated :)

 

[HallsofIvy]

They look perfectly good to me.

 

[forty]

love you :)