🛠️ JEE➗ Maths

If \(A\) is a square matrix of order 3 , then \(\left|\operatorname{Adj}\left(\operatorname{Adj} A^2\right)\right|\) is:

Q1 FREE PREVIEW

If \(A\) is a square matrix of order 3 , then \(\left|\operatorname{Adj}\left(\operatorname{Adj} A^2\right)\right|\) is:

a

\(|A|^2\)

b

\(|A|^4\)

c

\(|A|^8\)

d

\(|A|^{16}\)

✓ Correct answer: c)

\(|A|^8\)

Explanation

\(\text{ As }|adj(adj\mathrm{A})|=|\mathrm{A}{|}^{{(\mathrm{n}-1)}^{2}}\text{,}\\ \text{where }\mathrm{n}\text{ is the order of the determinant. }\\ \text{ So, }\left|adj\left(adj{\mathrm{A}}^{2}\right)\right|={\left|{\mathrm{A}}^{2}\right|}^{(3-1{)}^{2}}\\ ={\left|{\mathrm{A}}^{2}\right|}^{4}=|\mathrm{A}{|}^{8}\)

Practice more JEE Maths PYQs

See every question on Determinants, or browse the full JEE question bank.

See all questions on Determinants →