Question

If A = `[(1,2),(3,-5)]`, then A^-1 = ?

Options

• `[(-5,-2),(-3,1)]`

• `[(5/11,2/11),(3/11,(-1)/11)]`

• `[((-5)/11,(-2)/11),((-3)/11,1/11)]`

• `[(5,2),(3,-1)]`

Answer 1

`[(5/11,2/11),(3/11,(-1)/11)]`

Explanation:

If A = `[(a,b),(c,d)]` and ad - bc ≠ 0, then

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

∴ `"A"^-1 = ([(-5,-2),(-3,1)])/(-11)`

= `[(5/11,2/11),(3/11,(-1)/11)]`