Question

If A = `[(2, -3),(x, y)]` and A² = I, find x and y.

Answer 1

A = `[(2, -3),(x, y)]`

I = `[(1, 0),(0, 1)]`

A² = `[(2, -3),(x, y)] xx [(2, -3),(x, y)]`

= `[(2 xx 2 + (-3) xx x, 2 xx (-3) + (-3) xx y),(x xx 2 + y xx x, x xx (-3) + y xx y)]`

= `[(4 - 3x, -6 - 3y),(2x + xy, -3x + y^2)]`

A² = I

`[(4 - 3x, -6 - 3y),(2x + xy, -3x + y^2)] = [(1, 0),(0, 1)]`

Equating corresponding elements

From (1, 1):

4 − 3x = 1

3x = 3

x = 1

From (1, 2):

− 6 − 3y = 0

3y = 6

y = −2