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