Find the Inverse [[-7,12],[-4,7]]^2

Problem

([[−7,12],[−4,7]]2)(−1)

Solution

1. Square the matrix by performing matrix multiplication of the given matrix with itself.

[[−7,12],[−4,7]]*[[−7,12],[−4,7]]=[[(−7)*(−7)+(12)*(−4),(−7)*(12)+(12)*(7)],[(−4)*(−7)+(7)*(−4),(−4)*(12)+(7)*(7)]]

2. Simplify the entries of the resulting matrix.

[[49−48,−84+84],[28−28,−48+49]]=[[1,0],[0,1]]

3. Identify the identity matrix as the result of the squaring operation.

[[−7,12],[−4,7]]2=I

4. Find the inverse of the identity matrix, which is the identity matrix itself.

I(−1)=I

Final Answer

([[−7,12],[−4,7]]2)(−1)=[[1,0],[0,1]]

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