Help Me Solve Matrix: Show B†A† = C†

[theacerf1]

Please HELP! Matrix!

Please help me with the below question! I have no idea how to solve this, if someone could please help me with a solution and explain what they did and how they did it, it would be such a BIG help! Thanks! :)


If A is an m×n matrix with (i, j)-entry aij , let A† be the n×m matrix with (i, j)-entry
aji. Show that

(i) if the product C = AB is defined, then so is B†A†,
(ii) B†A† = C†.

 

[elabed haidar]

well can you define B ??

 

[theacerf1]

Thats all the question says, so confused

 

[elabed haidar]

since C =AB is defined then the matrix AB is defined thus B is defined to be a n x c matrix where c is any number
since A† be the n×m matrix so B† is defined as a c x n so B† A† is defined as a c x m matrix therefore B† A† is defined

 

[elabed haidar]

okay second part comes from the first part if C is AB then it is a m x c matrix use A† is an n x m matrix with (i, j)-entry aij mulitply with B† by saying that B is a c x n matrix with (i, j)-entry bij and mulitply them you will get your answer but one note i didnt give you details so you have to define each matrix

 

[Otischen]

can anyone elaborate on this? i still don't get Elabed Haidar's answer. Sorry