Examples

$3$

Step 1

The identity matrix or unit matrix of size $3$ is the $3 \times 3$ square matrix with ones on the main diagonal and zeros elsewhere.

$[\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$

Step 2

Multiply the scalar $3$ by the identity matrix.

$3 [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$

Step 3

Simplify.

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Step 3.1

Multiply $3$ by each element of the matrix.

$[\begin{array}{c} 3 \cdot 1 & 3 \cdot 0 & 3 \cdot 0 \\ 3 \cdot 0 & 3 \cdot 1 & 3 \cdot 0 \\ 3 \cdot 0 & 3 \cdot 0 & 3 \cdot 1 \end{array}]$

Step 3.2

Simplify each element in the matrix.

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Step 3.2.1

Multiply $3$ by $1$ .

$[\begin{array}{c} 3 & 3 \cdot 0 & 3 \cdot 0 \\ 3 \cdot 0 & 3 \cdot 1 & 3 \cdot 0 \\ 3 \cdot 0 & 3 \cdot 0 & 3 \cdot 1 \end{array}]$

Step 3.2.2

Multiply $3$ by $0$ .

$[\begin{array}{c} 3 & 0 & 3 \cdot 0 \\ 3 \cdot 0 & 3 \cdot 1 & 3 \cdot 0 \\ 3 \cdot 0 & 3 \cdot 0 & 3 \cdot 1 \end{array}]$

Step 3.2.3

Multiply $3$ by $0$ .

$[\begin{array}{c} 3 & 0 & 0 \\ 3 \cdot 0 & 3 \cdot 1 & 3 \cdot 0 \\ 3 \cdot 0 & 3 \cdot 0 & 3 \cdot 1 \end{array}]$

Step 3.2.4

Multiply $3$ by $0$ .

$[\begin{array}{c} 3 & 0 & 0 \\ 0 & 3 \cdot 1 & 3 \cdot 0 \\ 3 \cdot 0 & 3 \cdot 0 & 3 \cdot 1 \end{array}]$

Step 3.2.5

Multiply $3$ by $1$ .

$[\begin{array}{c} 3 & 0 & 0 \\ 0 & 3 & 3 \cdot 0 \\ 3 \cdot 0 & 3 \cdot 0 & 3 \cdot 1 \end{array}]$

Step 3.2.6

Multiply $3$ by $0$ .

$[\begin{array}{c} 3 & 0 & 0 \\ 0 & 3 & 0 \\ 3 \cdot 0 & 3 \cdot 0 & 3 \cdot 1 \end{array}]$

Step 3.2.7

Multiply $3$ by $0$ .

$[\begin{array}{c} 3 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 3 \cdot 0 & 3 \cdot 1 \end{array}]$

Step 3.2.8

Multiply $3$ by $0$ .

$[\begin{array}{c} 3 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 3 \cdot 1 \end{array}]$

Step 3.2.9

Multiply $3$ by $1$ .

$[\begin{array}{c} 3 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 3 \end{array}]$

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