Let A , B and C are n × n matrices such that A = 2 , B = 3 and C = 5 . If 2 A 2 3 B 5 C - 1 = 1728 125 , then the value of n is equal to

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Question: Answered & Verified by Expert

Let

A, B

and

C

are

n \times n

matrices such that

|A| = 2, |B| = 3

and

|C| = 5 .

If

|{(2 A)}^{2} (3 B) {(5 C)}^{- 1}| = \frac{1728}{125}

, then the value of

n

is equal to

MathematicsDeterminantsJEE Main

Options:

A $2$
B $3$
C $4$
D $6$

Solution:

2517 Upvotes Verified Answer

The correct answer is:

2

|{(2 A)}^{2} (3 B) {(5 C)}^{- 1}| = \frac{{|2 A|}^{2} |3 B|}{|5 C|} = \frac{2^{2 n} 3^{n}}{5^{n}} \frac{{|A|}^{2} |B|}{|C|}

\Rightarrow {(\frac{12}{5})}^{n + 1} = {(\frac{12}{5})}^{3} \Rightarrow n = 2

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