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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

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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.

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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.

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