Find the Result of 2 Times the 2x2 Identity Matrix 2

Problem

2⋅(I_2)

Solution

1. Identify the 2×2 identity matrix, denoted as (I_2) which has ones on the main diagonal and zeros elsewhere.

(I_2)=([1,0],[0,1])

2. Apply scalar multiplication by multiplying every element inside the matrix by the scalar 2

2⋅([1,0],[0,1])=([2⋅1,2⋅0],[2⋅0,2⋅1])

3. Simplify the products within the matrix to find the final result.

([2⋅1,2⋅0],[2⋅0,2⋅1])=([2,0],[0,2])

Final Answer

2⋅([1,0],[0,1])=([2,0],[0,2])

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