Question

If A = `[(2,  -3, 3),(2, 2, 3),(3, "p", 2)]` and A^–1 = `[(-2/5, 0, 3/5),(-1/5, 1/5, "q"),(2/5, 1/5, -2/5)]`, then ______.

Options

• p = 1, q = 2

• p = – 2, q = 0

• p = 1, q = – 2

• p = – 3, q = 2

Answer 1

If A = `[(2,  -3, 3),(2, 2, 3),(3, "p", 2)]` and A^–1 = `[(-2/5, 0, 3/5),(-1/5, 1/5, "q"),(2/5, 1/5, -2/5)]`, then p = – 2, q = 0.

Explanation:

AA^–1 = I

∴ `[(2,  -3, 3),(2, 2, 3),(3, "p", 2)] [(-2/5, 0, 3/5),(-1/5, 1/5, "q"),(2/5, 1/5, -2/5)] = [(1, 0, 0),(0, 1, 0),(0, 0, 1)]`

⇒ `[(1, 0, -3"q"),(0, 1, 2"q"),((-2 - "p")/5, ("p" + 2)/5, 1 + "pq")] = [(1, 0, 0),(0, 1, 0),(0, 0, 1)]`

 ∴ By equality of matrices, we get

– 3q = 0 and `("p" + 2)/5` = 0

⇒ p = – 2, q = 0