Let A and B are two non-singular matrices of order 3 such that A + B = 2 I and A - 1 + B - 1 = 3 I , then A B is equal to (where, I is the identity matrix of order 3 )

Question

Let A and B are two non-singular matrices of order 3 such that A + B = 2 I and A - 1 + B - 1 = 3 I , then A B is equal to (where, I is the identity matrix of order 3 ), A, B, 2 I 3, 2 I

MARKS App · Accepted Answer

Given A + B = 2 I ... (i) and A - 1 + B - 1 = 3 I ...(ii) Multiplying by matrix A in eq. (ii), we get, A A - 1 + A B - 1 = 3 A I I + A B - 1 = 3 A Now, multiplying by matrix B , we get, I B + A B - 1 B = 3 A B ⇒ B + A = 3 A B ⇒ 3 A B = 2 I (from (i)) ⇒ A B = 2 I 3

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