Find the Inverse [[a,b],[c,d]]

Problem

[[a,b],[c,d]]

Solution

1. Calculate the determinant of the matrix, which is the product of the main diagonal elements minus the product of the off-diagonal elements.

det(=)*a*d−b*c

2. Check for invertibility by ensuring the determinant is non-zero. If a*d−b*c≠0 the inverse exists.

3. Swap the elements on the main diagonal (a and d.

[[d,b],[c,a]]

4. Change the signs of the elements on the off-diagonal (b and c.

[[d,−b],[−c,a]]

5. Multiply the matrix by the reciprocal of the determinant to find the inverse.

1/(a*d−b*c)*[[d,−b],[−c,a]]

Final Answer

[[a,b],[c,d]](−1)=1/(a*d−b*c)*[[d,−b],[−c,a]]

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