Question

If A = `[(-1, 1),(a, b)]` and A² = I, find a and b.

Answer 1

A = `[(-1, 1),(a, b)]`

A²= `[(-1, 1),(a, b)][(-1, 1),(a, b)]`

= `[((-1) xx (-1) + 1 xx a, -1 xx 1 + 1 xx b),(a xx (-1) + b xx a, a xx 1 + b xx b)]`

= `[(1 + a, -1 + b),(-a + ab, a + b^2)]`

It is given that A² = I.

∴ `[(1 + a, -1 + b),(-a + ab, a + b^2)] = [(1, 0),(0, 1)]`

Comparing the corresponding elements, we get,

1 + a = 1

Therefore, a = 0

–1 + b = 0

Therefore, b = 1