Question

How do you find the inverse of `A=``((6, 3), (4, 6))`?

Answer 1

`((1/4,-1/8),(-1/6,1/4))`

Explanation:

For any matrix

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

then the inverse matrix is found as follows:

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

ad - bc , is called the 'determinant ,and it's value determines whether an inverse matrix exists or not.

If tdet(A) = 0 ,then inverse does not exist and matrix is said to be singular.

using the values from the question :

ad - bc = `(6xx6) - (3 xx4) = "24 , hence matrix exists"`

`1/24((6,-3),(-4,6)) = ((1/4,-1/8),(-1/6,1/4))`