Question

# Find the inverse of matrices begin{bmatrix}8 & 6 5 & 4end{bmatrix}

Matrices
Find the inverse of matrices
$$\begin{bmatrix}8 & 6 \\5 & 4\end{bmatrix}$$

2021-03-03
Step 1
here given matrix
$$A=\begin{bmatrix}8 & 6 \\5 & 4\end{bmatrix}$$
Use the formula for $$2 \times 2$$ matrices, which states
if $$A=\begin{bmatrix}a & b \\c & d \end{bmatrix}$$
Thus $$A^{-1}=\frac{1}{ad-bc}\begin{bmatrix}d & -b \\-c & a \end{bmatrix}$$
Step 2
Thus
$$A^{-1}=\frac{1}{2}\begin{bmatrix}4 & -6 \\-5 & 8 \end{bmatrix}$$
$$=\begin{bmatrix}2 & -3 \\\frac{-5}{2} & 4 \end{bmatrix}$$