Multiply the Matrices

Problem

[[1,0,0],[0,1,0],[0,0,1]]*[[1,0,0],[0,1,1],[0,1,1]]

Solution

1. Identify the matrices being multiplied. The first matrix is the 3×3 identity matrix, denoted as I

2. Apply the property of the identity matrix. For any square matrix A of the same dimension, the product I*A=A

3. Calculate the individual entries using the dot product of rows from the first matrix and columns from the second matrix to verify.

4. Row 1 calculation:

(1⋅1)+(0⋅0)+(0⋅0)=1

(1⋅0)+(0⋅1)+(0⋅1)=0

(1⋅0)+(0⋅1)+(0⋅1)=0

5. Row 2 calculation:

(0⋅1)+(1⋅0)+(0⋅0)=0

(0⋅0)+(1⋅1)+(0⋅1)=1

(0⋅0)+(1⋅1)+(0⋅1)=1

6. Row 3 calculation:

(0⋅1)+(0⋅0)+(1⋅0)=0

(0⋅0)+(0⋅1)+(1⋅1)=1

(0⋅0)+(0⋅1)+(1⋅1)=1

Final Answer

[[1,0,0],[0,1,0],[0,0,1]]*[[1,0,0],[0,1,1],[0,1,1]]=[[1,0,0],[0,1,1],[0,1,1]]

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