Simplify the Matrix [[2,3],[4,5]][[2,3],[6,5]]

Problem

[[2,3],[4,5]]*[[2,3],[6,5]]

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)+3*(6)=4+18=22

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

2*(3)+3*(5)=6+15=21

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

4*(2)+5*(6)=8+30=38

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

4*(3)+5*(5)=12+25=37

6. Combine the results into the resulting matrix.

Final Answer

[[2,3],[4,5]]*[[2,3],[6,5]]=[[22,21],[38,37]]

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