Question

Select the correct answer.

Which matrix is the product of a 3 × 3 identity matrix and the scalar 3?

Answer 1

Option C:

`\left[\begin{array}{lll}3 & 0 & 0 \\0 & 3 & 0 \\0 & 0 & 3\end{array}\right]`

Solution:

3 × 3 identity matrix is

`I=\left[\begin{array}{lll}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{array}\right]`

Scalar element = 3

Product of 3 × 3 identity matrix and scalar 3 is

`3I=3\left[\begin{array}{lll}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{array}\right]`

3 multiplied into inside the matrix, we get

`3I=\left[\begin{array}{lll}3 & 0 & 0 \\0 & 3 & 0 \\0 & 0 & 3\end{array}\right]`

The product of 3 × 3 identity matrix and scalar 3 is

`\left[\begin{array}{lll}3 & 0 & 0 \\0 & 3 & 0 \\0 & 0 & 3\end{array}\right]`

Option C is the correct answer.