Using the Formula to Find the Multiplicative Inverse of Matrix A

Use the formula to find the multiplicative inverse of

A = [\begin{matrix} 1 & −2 \\ 2 & −3 \end{matrix}]

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Using the formula, we have

$\begin{array}{l} A^{−1} = \frac{1}{(1) (−3) - (−2) (2)} [\begin{matrix} −3 & 2 \\ −2 & 1 \end{matrix}] \\ = \frac{1}{−3 + 4} [\begin{matrix} −3 & 2 \\ −2 & 1 \end{matrix}] \\ = [\begin{matrix} −3 & 2 \\ −2 & 1 \end{matrix}] \end{array}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Use the formula to find the inverse of matrix $A .$ Verify your answer by augmenting with the identity matrix.

A = [\begin{matrix} 1 & −1 \\ 2 & 3 \end{matrix}]

How did it go?