CUET Preparation Today
If A and B are invertible matrices of same order, then which one of the following is NOT true? |
$(AB)^{-1}= B^{-1} A^{-1}$ $adj\, (AB) = (adj\, A) (adj\, B)$ $adj\, A^T = (adj\, A)^T$ $|A^{-1}| = (|A|)^{-1}$ |
$adj\, (AB) = (adj\, A) (adj\, B)$ |
The correct answer is Option (2) → $adj\, (AB) = (adj\, A) (adj\, B)$ Check each identity. (A) $(AB)^{-1}=B^{-1}A^{-1}$ is always true. (B) $\text{adj}(AB)=\text{adj}(A)\text{adj}(B)$ is false because the correct identity is $\text{adj}(AB)=\text{adj}(B)\text{adj}(A)$. (C) $\text{adj}(A^{T})=(\text{adj}A)^{T}$ is true. (D) $|A^{-1}|=(|A|)^{-1}$ is true. Final answer: $\text{adj}(AB)=(\text{adj}A)(\text{adj}B)$ is NOT true |
