How do you find the inverse of ((7, -4),(-5, 3))?

Feb 28, 2016

$\left(\begin{matrix}3 & 4 \\ 5 & 7\end{matrix}\right)$

Explanation:

For a 2X2 matrix A , the inverse is found as follows:

For a matrix A = $\left(\begin{matrix}a & b \\ c & d\end{matrix}\right)$

Then the inverse ${A}^{-} 1 = \frac{1}{a d - b c} \left(\begin{matrix}d & - b \\ - c & a\end{matrix}\right)$

(ad - bc) is the determinant of the matrix , and if equal to zero, then the matrix has no inverse and is said to be singular.

here a = 7 b = -4 , c = -5 and d = 3

ad - bc =$\left(7 \times 3\right) - \left(- 4 \times - 5\right) = 21 - 20 = 1$

hence an inverse matrix exists

$\Rightarrow {A}^{-} 1 = \left(\begin{matrix}3 & 4 \\ 5 & 7\end{matrix}\right)$