Chapter 3, Problem 7SGR

To determine

To fill the blank space: The ……………. matrix is a square matrix that, when multiplied by another matrix, equals the same matrix.

Answer to Problem 7SGR

The …identity matrix…………. matrix is a square matrix that, when multiplied by another matrix, equals the same matrix.

Explanation of Solution

Given information :

Given a square matrix that, when multiplied by another matrix, equals the same matrix.

Let $I=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$ be an identity matrix of dimension $2\times 2$ and $A=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$ be another matrix of dimension $2\times 2$ .

  $\text{Now}\text{consider}AI=IA=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$

Thus, identity matrix has a special that, when multiplied by another matrix, equals the same matrix.

Hence, the …identity matrix…………. matrix is a square matrix that, when multiplied by another matrix, equals the same matrix.