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

Problem

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

Solution

1. Identify the matrix as the 2×2 identity matrix, denoted as I

2. Apply the property of identity matrices, which states that any power of the identity matrix is equal to the identity matrix itself.

3. Perform matrix multiplication to verify the result by multiplying the matrix by itself.

[[1,0],[0,1]]*[[1,0],[0,1]]=[[(1)*(1)+(0)*(0),(1)*(0)+(0)*(1)],[(0)*(1)+(1)*(0),(0)*(0)+(1)*(1)]]

4. Simplify the arithmetic within the resulting matrix.

[[1+0,0+0],[0+0,0+1]]=[[1,0],[0,1]]

Final Answer

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

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