Practicing Success
Let A be a square matrix of order n. Statement-1: $|adj (adj\, A)|=|A|^{(n-1)^2}$ Statement-2: $adj (adj\, A) =|A|^{n-2} A$ |
Statement-1 is True, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement-1. Statement-1 is True, Statement-2 is False. Statement-1 is False, Statement-2 is True. |
Statement-1 is True, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. |
Statement-1 is true $∴|adj (adj\, A)|=||A|^{n-2}A|=|A|^{(n-2)n}|A|$ $⇒|adj (adj\, A)|=|A|^{n^2-2n+1}=|A|^{(n-1)^2}$ |