Chapter 8.3, Problem 74E

To determine

Whether the given statement “when the product of two square matrices is the identity matrix, the matrices are inverses of one another” is true or false.

Answer to Problem 74E

The given statement is true.

Explanation of Solution

Given information:

Givenstatement is “when the product of two square matrices is the identity matrix, the matrices are inverses of one another”.

According to definition of invertible matrices, two square matrices $A\text{and}B$ are said to be invertible if $A\times B=B\times A=I$

Thus, the product of two square matrices is the identity matrix.

Therefore,the matrices are inverses of one another.

Hence, the given statement is true.