Find the Determinant of the Resulting Matrix [[81,32],[162,48]][[-3,0],[0,-2]]

Problem

det([[81,32],[162,48]]*[[−3,0],[0,−2]])

Solution

1. Identify the property of determinants for the product of two matrices A and B which states that det(A*B)=det(A)*det(B)

2. Calculate the determinant of the first matrix A=[[81,32],[162,48]] using the formula a*d−b*c

det(A)=(81)*(48)−(32)*(162)

det(A)=3888−5184

det(A)=−1296

3. Calculate the determinant of the second matrix B=[[−3,0],[0,−2]] using the formula a*d−b*c

det(B)=(−3)*(−2)−(0)*(0)

det(B)=6

4. Multiply the two determinants together to find the determinant of the resulting matrix.

det(A*B)=(−1296)*(6)

det(A*B)=−7776

Final Answer

det([[81,32],[162,48]]*[[−3,0],[0,−2]])=−7776

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