Consider the following statements in respect of a non-singular matrix A of order n: 1. A(adjA^{T})=A(adjA)^{T} 2. If A^{2}=A, then A is identity matrix of order n 3. If A^{3}=A, then A is identity matrix of order n Which of the statements given above are correct?

Explanation

Statement 1 is true because adj(A^T) = (adjA)^T is a standard property of the adjoint. Statement 2 is true because A is non-singular (A^{-1} exists), so multiplying A^2=A by A^{-1} gives A=I. Statement 3 is false because A^3=A implies A^2=I, which means A is an involutory matrix, not necessarily the identity matrix. Hence, statements 1 and 2 are correct.

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