CPM Homework Help : PC3 Problem 10-67

Verify that for the matrix $M = \left[ \begin{array} { l l } { 3 } & { 4 } \\ { 1 } & { 2 } \end{array} \right]$ the inverse matrix is $M^{-1}=\left[ \begin{array} { l l } { 3 } & { 4 } \\ { 1 } & { 2 } \end{array} \right]$ by showing that $M^{−1}M=MM^{−1}=I$ .

Step 1:

$\begin{bmatrix}3&4\\1&2\end{bmatrix}\begin{bmatrix}1&-2\\-0.5&1.5\end{bmatrix}=\begin{bmatrix}3(1)+4(-0.5)&3(-2)+4(1.5)\\1(1)+2(-0.5)&1(-2)+2(1.5)\end{bmatrix}$