Question

Solve the following :

If A = `[(-3, 2),(2, 4)], "B" = [(1, "a"), ("b", 0)]` and (A + B) (A – B) = A² – B², find a and b.

Answer 1

(A + B) (A – B) = A² – B²
∴ A² – AB + BA – B² = A² – B²
∴ –AB + BA = 0
∴ AB = BA

∴ `[(-3, 2),(2, 4)][(1, "a"),("b", 0)] = [(1, "a"),("b", 0)][(-3, 2),(2, 4)]`

∴ `[(-3 +2"b", -3"a" + 0),(2 + 4"b", 2"a" + 0)] = [(-3 + 2"a", 2 + 4"a"),(-3"b" + 0, 2"b" + 0)]`

∴ By equality of matrices, we get
– 3a = 2 + 4a
∴ 7a = – 2
∴ a = `(-2)/(7)`
and 2 + 4b = – 3b
∴ 7b = – 2
∴ b = `(-2)/(7)`.