Simplify the Matrix [[2,0],[3,1]]^2

Problem

[[2,0],[3,1]]2

Solution

1. Identify the operation as matrix squaring, which means multiplying the matrix by itself.

A2=[[2,0],[3,1]]*[[2,0],[3,1]]

2. Calculate the element in the first row, first column by multiplying the first row of the first matrix by the first column of the second matrix.

(2⋅2)+(0⋅3)=4

3. Calculate the element in the first row, second column by multiplying the first row of the first matrix by the second column of the second matrix.

(2⋅0)+(0⋅1)=0

4. Calculate the element in the second row, first column by multiplying the second row of the first matrix by the first column of the second matrix.

(3⋅2)+(1⋅3)=9

5. Calculate the element in the second row, second column by multiplying the second row of the first matrix by the second column of the second matrix.

(3⋅0)+(1⋅1)=1

6. Combine the results into the resulting 2×2 matrix.

[[4,0],[9,1]]

Final Answer

[[2,0],[3,1]]2=[[4,0],[9,1]]

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