Algebra

Matrices & Determinants

Medium

applied

If A is a square matrix of order 3 such that $|A| = 3$ , then $|adj(adj A)|$ is equal to:

1/3

✅ Correct Option: 4

Given: A is a square matrix of order 3 and $|A| = 3$

For any square matrix M of order n:

$|adj(M)| = |M|^{n-1}$

Since A is of order $n = 3$ :

$|adj(A)| = |A|^{n-1}$

$|adj(A)| = |A|^{3-1}$

$|adj(A)| = |A|^2$

$|adj(A)| = (3)^2$

$|adj(A)| = 9$

Let $B = adj(A)$ , so $|B| = 9$

Finding $|adj(adj A)| = |adj(B)|$ :

$|adj(B)| = |B|^{n-1}$

$|adj(B)| = |B|^{3-1}$

$|adj(B)| = |B|^2$

$|adj(B)| = (9)^2$

$|adj(B)| = 81$

Therefore, $|adj(adj A)| = 81$

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Choose the correct answer from the options given below:

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Choose the correct answer from the options given below:

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Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If A is a square matrix of order 3 such that $|A| = 3$ , then $|adj(adj A)|$ is equal to: