## Linear Algebra and Its Applications, Review Exercise 1.2

Review exercise 1.2. Given matrices $A$ and $B$ as follows $A = \begin{bmatrix} 1&0 \\ 2&1 \end{bmatrix} \qquad B = \begin{bmatrix} 1&2 \\ 0&1 \end{bmatrix}$

find the products $AB$ and $BA$, the inverses $A^{-1}$, $B^{-1}$, and $(AB)^{-1}$. $AB = \begin{bmatrix} 1&0 \\ 2&1 \end{bmatrix} \begin{bmatrix} 1&2 \\ 0&1 \end{bmatrix} = \begin{bmatrix}1&2 \\ 2&5 \end{bmatrix}$ $BA = \begin{bmatrix} 1&2 \\ 0&1 \end{bmatrix} \begin{bmatrix} 1&0 \\ 2&1 \end{bmatrix} = \begin{bmatrix}5&2 \\ 2&1 \end{bmatrix}$ $A^{-1} = \frac{1}{1 \cdot 1 - 2 \cdot 0} \begin{bmatrix} 1&-0 \\ -2&1 \end{bmatrix} = \begin{bmatrix} 1&0 \\ -2&1 \end{bmatrix}$ $B^{-1} = \frac{1}{1 \cdot 1 - 2 \cdot 0} \begin{bmatrix} 1&-2 \\ -0&1 \end{bmatrix} = \begin{bmatrix} 1&-2 \\ 0&1 \end{bmatrix}$ $(AB)^{-1} = B^{-1}A^{-1} = \begin{bmatrix} 1&-2 \\ 0&1 \end{bmatrix} \begin{bmatrix} 1&0 \\ -2&1 \end{bmatrix} = \begin{bmatrix} 5&-2 \\ -2&1 \end{bmatrix}$

NOTE: This continues a series of posts containing worked out exercises from the (out of print) book Linear Algebra and Its Applications, Third Edition by Gilbert Strang.

If you find these posts useful I encourage you to also check out the more current Linear Algebra and Its Applications, Fourth Edition , Dr Strang’s introductory textbook Introduction to Linear Algebra, Fourth Edition and the accompanying free online course, and Dr Strang’s other books .

This entry was posted in linear algebra. Bookmark the permalink.