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Match the LIST-I with LIST-II

LIST-I
Matrix A
LIST-II
∣adj A∣\vert adj\,A \vert
A.[123025001]\begin{bmatrix}1 & 2 & 3\\ 0 & 2 & 5\\ 0 & 0 & 1\end{bmatrix}I.99
B.[3−1401200−1]\begin{bmatrix}3 & -1 & 4\\ 0 & 1 & 2\\ 0 & 0 & -1\end{bmatrix}II.1616
C.[42−30−25001]\begin{bmatrix}4 & 2 & -3\\ 0 & -2 & 5\\ 0 & 0 & 1\end{bmatrix}III.6464
D.[253021001]\begin{bmatrix}2 & 5 & 3\\ 0 & 2 & 1\\ 0 & 0 & 1\end{bmatrix}IV.44

Choose the correct answer from the options given below:

Solution

✅ Correct Option: 4

For order 33, ∣adjA∣=∣A∣2|adj A| = |A|^2. All four matrices are upper triangular, so their determinants are the products of diagonal entries: 22, −3-3, −8-8 and 44. Squaring gives 44, 99, 6464 and 1616.

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