Q42 of 256 Page 7

A matrix A of order 3 × 3 is such that |A| = 4. Find the value of |2A|.

We are given that,

Order of matrix A = 3


|A| = 4


We need to find the value of |2A|.


By property of determinant of matrix,


|KA| = Kn|A|


Where, order of the matrix A is n.


Similarly,


|2A| = 23|A|


[∵, Order of matrix A = 3]


⇒ |2A| = 8|A|


Substituting the value of |A| in the above equation,


⇒ |2A| = 8 × 4


⇒ |2A| = 32


Thus, the value of |2A| is 32.


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