Multiply the Matrices

Problem

[[−1,1,−3],[−9,8,7],[−8,−2,−2]]*[[1,0,0],[0,1,0],[0,0,1]]

Solution

1. Identify the second matrix as the 3×3 identity matrix, denoted as I

2. Apply the property of the identity matrix, which states that for any square matrix A of the same dimension, A*I=A

3. Perform the multiplication by calculating the dot product of each row of the first matrix with each column of the identity matrix.

4. Calculate the first row:

(−1)*(1)+(1)*(0)+(−3)*(0)=−1

(1)*(0)+(1)*(1)+(−3)*(0)=1

(−1)*(0)+(1)*(0)+(−3)*(1)=−3

5. Calculate the second row:

(−9)*(1)+(8)*(0)+(7)*(0)=−9

(−9)*(0)+(8)*(1)+(7)*(0)=8

(−9)*(0)+(8)*(0)+(7)*(1)=7

6. Calculate the third row:

(−8)*(1)+(−2)*(0)+(−2)*(0)=−8

(−8)*(0)+(−2)*(1)+(−2)*(0)=−2

(−8)*(0)+(−2)*(0)+(−2)*(1)=−2

Final Answer

[[−1,1,−3],[−9,8,7],[−8,−2,−2]]*[[1,0,0],[0,1,0],[0,0,1]]=[[−1,1,−3],[−9,8,7],[−8,−2,−2]]

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