Question

If A = `[(3, x),(0, 1)]` and B = `[(9, 16),(0, -y)]`, find x and y when A² = B.

Answer 1

Given A = `[(3, x),(0, 1)]`, B = `[(9, 16),(0, -y)]` and A² = B

Now, A² = A × A

= `[(3, x),(0, 1)] xx [(3, x),(0, 1)]`

= `[(3 xx 3 + x xx 0, 1 xx x + x xx 1),(0 xx 3 + 1 xx 0, 0 xx x + 1 xx 1)]`

= `[(9 + 0, 3x + x),(0 + 0, 0 + 1)]`

= `[(9, 4x),(0, 1)]`

We have A² = B

Two matrices are equal if each and every corresponding element is equal.

`=> [(9, 4x),(0, 1)] = [(9, 16), (0, -y)]`

`=>` 4x = 16 and 1 = –y

`=>` x = 4 and y = –1