Question

If A = `[(5, -4), (7, -5)]`, then 3A^-1 =  ______ 

Options

• `1/3`A

• 3A

• -3A

• -A

Answer 1

If A = `[(5, -4), (7, -5)]`, then 3A^-1 = -A 

Explanation:

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

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

∴ `A = [(5, -4), (7, -5)]`

`A^-1 = 1/3[(-5, 4), (-7, 5)]`

⇒ `3A^-1 = -[(5, -4), (7, -5)]`

= -A