If A and B are 9 times 3 matrices and C is a 6 times 9 matri

If A and B are 9 times 3 matrices, and C is a 6 times 9 matrix, which of the following are defined? A^T C^T B + A B^T AC CB C - A

A = 9 x 3
B = 9 x 3
C = 6 x 9

A)
AtCt
At will be 3 x 9
Ct will be 9 x 6
Notice the row of At = Column of Ct
So, yes, defined

B)
B + A
Of course defined as B and A have the same order

c)
Bt --> defined

d) AC :
A = 9 x 3
C = 6 x 9
Undefined as columns of A is not equal to rows of C

e) CB :
C = 6 x 9
B = 9 x 3
Yes, defined

f)
C - A :
Undefined as orders are not the same and thus,
these cannot be subtracted

DEfined :
Only A , B , C , E