If A= ( array ccc 1 & 0 & 0 0 & & 0 & & - array ) , then which of the following are correct? 1. A+ adj A is a null matrix 2. A⁻¹+ adj A is a null matrix 3. A-A⁻¹ is a null matrix Select the correct answer using the code given below :

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Quantrex Academy · Accepted Answer

Correct answer: D. 1,2 and 3

Concept: If a matrix A= ( array lll a₁₁ & a₁₂ & a₁₃ a₂₁ & a₂₂ & a₂₃ a₃₁ & a₃₂ & a₃₃ array ) then A^ = ( array lll a₁₁ & a₂₁ & a₃₁ a₁₂ & a₂₂ & a₃₂ a₁₃ & a₃₂ & a₃₃ array ) Explanation: If A= ( array ccc 1 & 0 & 0 0 & & 0 & & - array ) , the cofactor matrix of A is given by, cofactor (A)= ( array ccc -1 & 0 & 0 0 & - & - 0 & - & array ) So, adj A= ( array ccc -1 & 0 & 0 0 & - & - 0 & - & array ) (Transpose of cofactor matrix) adj A=-A _(i) adj A+A=0 is a null matrix So, statement 1 is correct. Now, expanding A along R

If A= ( array ccc 1 & 0 & 0 0 & & 0 & & - array ) , then which of the following are correct? 1. A+ adj A is a null matrix 2. A⁻¹+ adj A is a null matrix 3. A-A⁻¹ is a null matrix Select the correct answer using the code given below :

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