matrices question

[GreekGodX]

please help

[Lear]

please help

Is it B?

My understanding may be incorrect*

[S_R_K]

Edit: only B is correct

Hmmm.... I think both B and E are true.

Reasons for B

1. If AxBxC is defined, then BxC is defined. Hence number of columns in B = number of rows in C.
2. If CxAxB is defined, then its order is equal to the number of rows in C x number of columns in B.
(1) and (2) imply that CxAxB is a square matrix.

Reasons for E.

1. Matrix B has order 2x3.
2. If AxBxC is defined, then BxC is defined. Hence number of columns in B = number of rows in C.
3. If AxBxC is defined, then AxB is defined. Hence number of columns in A = number of rows in B.
4. AxBxC is a square matrix, hence number of rows in A = number of columns in C.

(1) and (2) imply that C has 3 rows. (1) and (3) imply that A has 3 columns. Hence, if CxA is defined, then it is a square matrix. *** Edit: this is wrong. (1) and (3) imply that A has 2 columns, hence CxA can not be a square matrix, even if it is defined.
(4) implies that CxA is defined.

I am confident that A, C, and D are all false, because it's easy to construct counterexamples.

Matrix A could be 2x2, in which case C must be a 3x2 matrix. This rules out options A, C, and D.

[galaxy21]

Hi here is what I worked out and how I got there. Hopefully it's clear...feel free to ask if you are unsure about anything!