My Math Forum Inverse of a 2x2 matrix

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 June 21st, 2012, 07:27 AM #1 Math Team   Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407 Inverse of a 2x2 matrix In case you didn't know . . . $\text{Find the inverse of: }\:A \;=\;\begin{bmatrix}a&b \\ \\ \\ c=&d\end{bmatrix}=$ $\text{[1] Switch the two on the main diagonal }(a\text{ and }d): \;\begin{bmatrix}d & . \\ \\ \\ . & a\end{bmatrix}$ $\text{[2] Change the signs of the other two: }\:\begin{bmatrix}. & -b \\ \\ \\ -c & . \end{bmatrix}$ $\text{[3] Divide everything by the determinant: }\:\begin{vmatrix}a=&b \\ \\ \\ c=&d\end{vmatrix} \:=\:ad\,-\,bc$ $\text{Therefore: }\:A^{-1} \;=\;\begin{bmatrix}\dfrac{d}{ad-bc} &\dfrac{-b}{ad-bc} \\ \\ \\ \dfrac{-c}{ad-bc}=&\dfrac{a}{ad-bc}\end{bmatrix}=$

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