Multiply the Matrices [[2,1],[3,2]]*[[2,-1],[-3,2]]

Problem

[[2,1],[3,2]]*[[2,−1],[−3,2]]

Solution

1. Identify the dimensions of the matrices. Both are 2×2 matrices, so their product will also be a 2×2 matrix.

2. Calculate the top-left element by multiplying the first row of the first matrix by the first column of the second matrix.

(2)*(2)+(1)*(−3)=4−3=1

3. Calculate the top-right element by multiplying the first row of the first matrix by the second column of the second matrix.

(2)*(−1)+(1)*(2)=−2+2=0

4. Calculate the bottom-left element by multiplying the second row of the first matrix by the first column of the second matrix.

(3)*(2)+(2)*(−3)=6−6=0

5. Calculate the bottom-right element by multiplying the second row of the first matrix by the second column of the second matrix.

(3)*(−1)+(2)*(2)=−3+4=1

6. Assemble the resulting matrix using the calculated values.

Final Answer

[[2,1],[3,2]]*[[2,−1],[−3,2]]=[[1,0],[0,1]]

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