Multiply the Matrices

Problem

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

Solution

1. Identify the dimensions of the matrices. Both are 4×4 matrices, so the resulting product will also be a 4×4 matrix.

2. Calculate the elements of the first row by multiplying the first row of the left matrix by each column of the right matrix.

(R_1)*(C_1)=(0)*(0)+(0)*(1)+(1)*(0)+(1)*(0)=0

(R_1)*(C_2)=(0)*(0)+(0)*(0)+(1)*(0)+(1)*(1)=1

(R_1)*(C_3)=(0)*(1)+(0)*(1)+(1)*(0)+(1)*(0)=0

(R_1)*(C_4)=(0)*(1)+(0)*(0)+(1)*(1)+(1)*(0)=1

3. Calculate the elements of the second row.

(R_2)*(C_1)=(1)*(0)+(0)*(1)+(1)*(0)+(0)*(0)=0

(R_2)*(C_2)=(1)*(0)+(0)*(0)+(1)*(0)+(0)*(1)=0

(R_2)*(C_3)=(1)*(1)+(0)*(1)+(1)*(0)+(0)*(0)=1

(R_2)*(C_4)=(1)*(1)+(0)*(0)+(1)*(1)+(0)*(0)=2

4. Calculate the elements of the third row.

(R_3)*(C_1)=(0)*(0)+(0)*(1)+(0)*(0)+(1)*(0)=0

(R_3)*(C_2)=(0)*(0)+(0)*(0)+(0)*(0)+(1)*(1)=1

(R_3)*(C_3)=(0)*(1)+(0)*(1)+(0)*(0)+(1)*(0)=0

(R_3)*(C_4)=(0)*(1)+(0)*(0)+(0)*(1)+(1)*(0)=0

5. Calculate the elements of the fourth row.

(R_4)*(C_1)=(0)*(0)+(1)*(1)+(0)*(0)+(0)*(0)=1

(R_4)*(C_2)=(0)*(0)+(1)*(0)+(0)*(0)+(0)*(1)=0

(R_4)*(C_3)=(0)*(1)+(1)*(1)+(0)*(0)+(0)*(0)=1

(R_4)*(C_4)=(0)*(1)+(1)*(0)+(0)*(1)+(0)*(0)=0

Final Answer

[[0,0,1,1],[1,0,1,0],[0,0,0,1],[0,1,0,0]]*[[0,0,1,1],[1,0,1,0],[0,0,0,1],[0,1,0,0]]=[[0,1,0,1],[0,0,1,2],[0,1,0,0],[1,0,1,0]]

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