For the multiplication of matrices as a binary operation on the set of all matrices of the form `[[a ,b],[-b ,a]],\ a ,\ b in R` the inverse of `[[2, 3],[-3, 2]]` is

Options

A. (a)`[[-2, 3],[-3,-2]]`
B. (b) `[2 3-3 2]`
C. (c) `[[frac{2}{13},frac{-3}{13}],[ frac{3}{13}, frac{2}{13}]]`
D. (d) `[[1, 0],[ 0, 1]]`

Answer

(c) `[[frac{2}{13},frac{-3}{13}],[ frac{3}{13}, frac{2}{13}]]`

Explanation

Let,

`A=[[a,b],[-b,a]]`

`I=[[x,y],[-y,x]]`

`A.I=I.A=A`

`[[a,b],[-b,a]][[x,y],[-y,x]]=[[x,y],[-y,x]]`

`Rightarrow ax-by=x``..(1)`

`Rightarrow ay+bx=y``..(2)`


Solving both equations, we get

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