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 - Concept and Vocabulary Check - Page 931: 5


If $ A=\left[ \begin{matrix} a & b \\ c & d \\ \end{matrix} \right]$, the matrix $ A $ is invertible if and only if $ ad-bc\ne 0$.

Work Step by Step

Consider the matrix $ A=\left[ \begin{matrix} a & b \\ c & d \\ \end{matrix} \right]$. Now, we will check if the matrix is invertible or not. The inverse of matrix $\left[ A \right]$ is equal to: ${{\left[ A \right]}^{-1}}=\frac{1}{ad-bc}\left[ \begin{matrix} d & -b \\ -c & a \\ \end{matrix} \right]$ Thus, $ ad-bc\ne 0$ for the matrix to be invertible.
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