Let A be the square matrix of order 3, then |kA|, where k is a scalar, is equal to: Option 1: 3k|A| Option 2: k^3|A| Option 3: k^2|A| Option 4: k|A|

The answer is 'k^3|A|'. View full solution:

CUET Mathematics - Let A be the square matrix of order 3, then |kA|, where k is a scalar, is equal to: | PYQs + Solutions

CUET Mathematics 2023 23 May Shift 3

Algebra

Easy

3k|A|

$k^3$ |A|

$k^2$ |A|

k|A|

✅ Correct Option: 2

Related questions:

14 May Shift 1

Let A be a non-singular matrix of order 3 and $|A| = 15$ , then $|adj A|$ is equal to

17 Aug Shift 2

Identify the correct statements.

(A) If $A$ is a non-singular matrix, then $A^{-1} = \frac{|A|}{(\text{adj } A)}$

(B) If $A$ is an invertible matrix then $\frac{1}{|A^{-1}|} = |A|$

(C) If $A$ and $B$ are two invertible matrices of the same order then $AB$ is also invertible matrix and $(BA)^{-1} = A^{-1}B^{-1}$

(D) If $A$ is an invertible matrix, then $A^T$ is also invertible and $(A^T)^{-1} = \frac{1}{(A^{-1})^T}$

Choose the correct answer from the options given below :

16 May Shift 1

$\Delta=\left|\begin{array}{ccc}1 & \cos x & 1 \\ -\cos x & 1 & \cos x \\ -1 & -\cos x & 1\end{array}\right|$

(A) $\Delta=2\left(1-\cos ^{2} x\right)$

(B) $\Delta=2\left(2-\sin ^{2} x\right)$

(D) Maximum value of $\Delta$ is $4$

Choose the correct answer from the options given below :