Find the Inverse of the Resulting Matrix [[-6,-44],[-1,32]][[15,-44],[-27,32]]

Problem

([[−6,−44],[−1,32]]*[[15,−44],[−27,32]])^(−1)

Solution

1. Multiply the two matrices to find the resulting matrix M

M=[[(−6)*(15)+(−44)*(−27),(−6)*(−44)+(−44)*(32)],[(−1)*(15)+(32)*(−27),(−1)*(−44)+(32)*(32)]]

2. Simplify the arithmetic for each entry of M

M=[[−90+1188,264−1408],[−15−864,44+1024]]

M=[[1098,−1144],[−879,1068]]

3. Calculate the determinant of matrix M denoted as det(M)

det(M)=(1098)*(1068)−(−1144)*(−879)

det(M)=1172664−1005576

det(M)=167088

4. Apply the inverse formula for a 2×2 matrix, which is M^(−1)=1/det(M)*[[d,−b],[−c,a]]

M^(−1)=1/167088*[[1068,1144],[879,1098]]

5. Simplify the fractions by dividing each term by the greatest common divisor.

M^(−1)=[[1068/167088,1144/167088],[879/167088,1098/167088]]

M^(−1)=[[89/13924,143/20886],[293/55696,183/27848]]

Final Answer

([[−6,−44],[−1,32]]*[[15,−44],[−27,32]])^(−1)=[[89/13924,143/20886],[293/55696,183/27848]]

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