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If A = (-1, 1),(A, B) and A^2 = I; Find a and B - Mathematics

Sum

If `A = [(-1, 1),(a, b)]` and `A^2 = I`; Find a and b

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Solution

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

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

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

It is given that `A^2 = 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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APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 9 Matrices
Exercise 9 (C) | Q 13 | Page 130
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