Question

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

Answer 1

`((3,4),(5,7))`

Explanation:

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

For a matrix A = `((a,b),(c,d))`

Then the inverse `A^-1 = 1/(ad-bc)((d,-b),(-c,a))`

(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 =`(7xx3) - (-4xx-5) = 21 -20 = 1`

hence an inverse matrix exists

`rArr A^-1 =( (3,4),(5,7))`