Solution Found!
True or false? (a) If A 2 is defined then A is necessarily square. (b) If AB and BA are
Chapter 1, Problem 1.4.42(choose chapter or problem)
True or false? (a) If A 2 is defined then A is necessarily square. (b) If AB and BA are defined then A and B are square. (c) If AB and BA are defined then AB and BA are square. (d) If AB = B then A = I.
Questions & Answers
QUESTION:
True or false? (a) If A 2 is defined then A is necessarily square. (b) If AB and BA are defined then A and B are square. (c) If AB and BA are defined then AB and BA are square. (d) If AB = B then A = I.
ANSWER:Step 1 of 5
(a)
The two matrix and can multiply only if number of columns of matrix is equal to the number of rows of matrix .
Let the matrix has rows and columns then matrix and are not compatible for multiplication because the multiplication rule is not applicable .
Hence, the product exists only if is the square matrix which is .
Therefore, the statement is true.