Question

If A = `[(2, -3),(x, y)]` and A2 = I, then the value of y is ______.

Options

• 1

• −1

• 2

• −2

Answer 1

If A = `[(2, -3),(x, y)]` and A2 = I, then the value of y is −2.

Explanation:

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)]`

set equal to identity matrics:

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

Compare corresponding elements

4 − 3x = 1

3x = 3

x = `3/3`

x = 1

−6 − 3y = 0

−3y = 6

y = `6/(−3)`

y = −2