Question

Let A be a square matrix of order 3 X 3. Write the value of I2AI, where IAI=4.

Answer 1

|A|=4
|2A|= 2³|A|
= 8 × 4
= 32

Answer 2

Given :

A is a square matrix of order 3×3

determinant of A is 4

To find :

Determinant of 2A i.e. |2A|

Solution :

•Consider the property ,

Let Determinant of matrix A of order n×n is |A| , if each and every term of matrix is multiplied by some constant K , then the determinant of the new matrix obtained will be K^n times determinant of A

•i.e. |kA| = K^n |A|

where , n is the order of matrix

•Now , determinant of matrix A = 4

i.e. |A| = 4 & order of matrix A is 3×3

•so, |2A| = 2³|A|

|2A| = 8|A|

|2A| = 32

•Hence , determinant of matrix 2A is 32 i.e. |2A| = 32