Question

How do you find the inverse of `A=``((3, 0), (4, 17))`?

Answer 1

The inverse is `A^(-1)=((1/3,0),(-4/51,1/17))`

Explanation:

The inverse of a matrix `((a,b),(c,d))` is `=1/(ad-bc)((d,-b),(-c,a))`

Here `A=((3,0),(4,17))`

The determinant of the matrix is `=(3*17-4*0)=51`

The determinant `!=0`, therefore it is invertible.

So, `A^(-1)=1/51((17,0),(-4,3))=((1/3,0),(-4/51,1/17))`

Verification
`A*A^(-1)=((3,0),(4,17))*((1/3,0),(-4/51,1/17)))=((1,0),(0,1))=I`
`I=` Identity Matrix