If A is a non-singular matrix of order 3 such that, adj(A), = 121, then, AA^T, is equal to: Option 1: 121 Option 2: 21 Option 3: 63 Option 4: 11

Answer: 121. Solution: Given that A is a non-singular matrix of order 3 and, adj(A), = 121. For any matrix of order n:, adj(A), =, A, ^(n-1) Since the matrix is of order 3, n = 3:, adj(A), =, A, ^(3-1), adj(A), =, A, ^2 Substituting the given value:, A, ^2 = 121, A, = ± 11 For any two matrices:, AB, =, A, x, B, Therefore:, AA^T, =, A, x, A^T, Since the determinant of a transpose equals the determinant of the original matrix:, A^T, =, A, Thus:, AA^T, =, A, x, A, AA^T, =, A, ^2, AA^T, =, A, ^2, AA^T, = (± 11)^2, AA^T, = 121 Therefore, AA^T, = 121.

Algebra

Matrices & Determinants

Medium

applied

If A is a non-singular matrix of order 3 such that $|adj(A)| = 121$ , then $|AA^T|$ is equal to:

121

✅ Correct Option: 1

Given that $A$ is a non-singular matrix of order 3 and $|adj(A)| = 121$ .

For any matrix of order $n$ :

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

Since the matrix is of order 3, $n = 3$ :

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

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

Substituting the given value:

$|A|^2 = 121$

$|A| = \pm 11$

For any two matrices:

$|AB| = |A| \times |B|$

Therefore:

$|AA^T| = |A| \times |A^T|$

Since the determinant of a transpose equals the determinant of the original matrix:

$|A^T| = |A|$

Thus:

$|AA^T| = |A| \times |A|$

$|AA^T| = |A|^2$

$|AA^T| = (\pm 11)^2$

$|AA^T| = 121$

Therefore, $|AA^T| = 121$ .

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Match List-I with List-II

List-I	List-II
(A) $\left\vert A \right\vert =$	(I) $\dfrac{1}{9}$
(B) $\left\vert A^{-1} \right\vert =$	(II) $81$
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Choose the correct answer from the options given below:

If A is a non-singular matrix of order 3 such that ∣adj(A)∣=121|adj(A)| = 121∣adj(A)∣=121, then ∣AAT∣|AA^T|∣AAT∣ is equal to:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If A is a non-singular matrix of order 3 such that $|adj(A)| = 121$ , then $|AA^T|$ is equal to: