Algebra

Matrices & Determinants

Medium

applied

Let $A$ be a non singular matrix of order $n \times n$ , Then $|\text{adj }(3A)|$ is equal to:

$3|A|^{n-1}$

$3^{n(n-1)}|A|^{n-1}$

$3^n|A|^{n-1}$

$3^n|A|^n$

✅ Correct Option: 2

For any matrix $B$ of order $n \times n$ :

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

For any scalar $k$ and matrix $A$ of order $n \times n$ :

$|kA| = k^n|A|$

Finding $|3A|$ :

$|3A| = 3^n|A|$

Applying the adjoint formula with $B = 3A$ :

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

Substituting $|3A| = 3^n|A|$ :

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

$= (3^n)^{n-1} \times (|A|)^{n-1}$

$= 3^{n(n-1)} \times |A|^{n-1}$

Therefore, $|\text{adj}(3A)| = 3^{n(n-1)}|A|^{n-1}$

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Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Let $A$ be a non singular matrix of order $n \times n$ , Then $|\text{adj }(3A)|$ is equal to: