Let A be a square matrix of order 3 then, 3A, is equal to Option 1: 3 A Option 2: 3^2 A Option 3: A, ^3 Option 4: 3^3 A

Answer: 3^3 A. Solution: For a square matrix A of order n, kA, = k^n, A, . Here n = 3 and k = 3, so, 3A, = 3^3, A, = 27, A, .

Algebra

Matrices & Determinants

Easy

common

Let A be a square matrix of order 3 then |3A| is equal to

3|A|

$3^2$ |A|

$|A|^3$

$3^3$ |A|

✅ Correct Option: 4

For a square matrix A of order $n$ , $|kA| = k^n |A|$ . Here $n = 3$ and $k = 3$ , so $|3A| = 3^3 |A| = 27|A|$ .

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