CUET Mathematics 2024 - If A is a square matrix of order 4 and |A|=4, then |2 A| will be : | PYQs + Solutions

CUET Mathematics 2024

Algebra

Matrices & Determinants

Easy

If $A$ is a square matrix of order $4$ and $|A|=4$ , then $|2 A|$ will be :

8

64

16

4

✅ Correct Option: 2

For determinants, when all elements of a matrix are multiplied by a scalar

k

, the determinant gets multiplied by

k^n

, where

n

is the order of the matrix.

For any

n×n

matrix

A

and scalar

k

|kA| = k^n|A|

In our problem:

|2A| = 2^4 · |A|

|2A| = 16 · 4

|2A| = 64

Related questions:

CUET Mathematics 2024

A

I

A^{2}=A

A(I-2 A)^{3}+2 A^{3}

CUET Mathematics 2024

A_{n \times n}

|\operatorname{adj} \mathrm{A}|=|\mathrm{A}|^{\mathrm{n}-1}

|\mathrm{A}|=|\operatorname{adj} \mathrm{A}|^{\mathrm{n}-1}

\mathrm{A}(\operatorname{adj} \mathrm{A})=|\mathrm{A}|

\left|\mathrm{A}^{-1}\right|=\frac{1}{|\mathrm{~A}|}

CUET Mathematics 2024

A

B

A B-B A