Question

If A = `[(2,3),(1,2)]`, B = `[(1,0),(3,1)]`, then B^-1A^-1 = ?

पर्याय

• `[(-2,-3),(-7,11)]`

• `[(2,-3),(-7,11)]`

• `[(2,3),(7,11)]`

• `[(-2,-3),(-7,-11)]`

Answer 1

`[(2,-3),(-7,11)]`

Explanation:

We have,

A = `[(2,3),(1,2)]`, and

B = `[(1,0),(3,1)]`

AB = `[(2,3),(1,2)] [(1,0),(3,1)]`

AB = `[(11,3),(7,2)]`

|AB| = 22 - 21 = 1

∴ `("AB")^-1 = [(2,-3),(-7,11)]`

∴ We know that,

B^-1 A^-1 = (AB)^-1

∴ B^-1 A^-1 = `[(2,-3),(-7,11)]`