Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 8 - Section 8.4 - Multiplicative Inverses of Matrices and Matrix Equations - Exercise Set - Page 933: 58


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Work Step by Step

Let the given $2\times2$ matrix be $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$ We can find its multiplicative inverse by switching the elements $a,d$, adding negative signs to $b,c$, and then dividing the new matrix by a factor of $(ad-bc)$. That is, $A^{-1}=\frac{1}{ad-bc}\begin{bmatrix} d & -b \\ -c & a \end{bmatrix}$
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