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

Question

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

MARKS Content Team · Accepted Answer

Correct answer: (C) 2I/3. Given A+B=2I ... (i) and A^(-1)+B^(-1)=3I ...(ii) Multiplying by matrix A in eq. (ii), we get, AA^(-1)+AB^(-1)=3AI I+AB^(-1)=3A Now, multiplying by matrix B, we get, IB+AB^(-1)B=3AB ⇒B+A=3AB ⇒3AB=2I (from (i)) ⇒AB=2I/3

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 $3$ )

Solution

More Matrices Questions

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

Solution

More Matrices Questions

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 $3$ )