If A = find the matrix B such that BA = I, where I is the unity matrix of order 2.

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KnowledgeBoat · Accepted Answer

Given, BA = I We know that B will be of order 2 × 2. So, let By definition of equality of matrices we get, 3a - b = 1 (...Eq 1) -4a + 2b = 0 ⇒ 4a = 2b ⇒ b = 2a (...Eq 2) 3c - d = 0 ⇒ d = 3c (...Eq 3) -4c + 2d = 1 (...Eq 4) Putting value of b from Eq 2 in Eq 1 ⇒ 3a - b = 1 ⇒ 3a - 2a = 1 ⇒ a = 1 ∴ a = 1, b = 2a = 2. Putting value of d from Eq 3 in Eq 4 ⇒ -4c + 2d = 1 ⇒ -4c + 2(3c) = 1 ⇒ -4c + 6c = 1 ⇒ 2c = 1 ⇒ c = ∴ c = , d = 3c = . Hence, the matrix B = .

Mathematics

If A = find the matrix B such that BA = I, where I is the unity matrix of order 2.

Matrices

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