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

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