If A is a square matrix such that $|A|=

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Determinants

Question:

If A is a square matrix such that $|A|= 2$, then for any positive integer n, $|A^n|$ is equal to

Options:

$2^n$

$n^2$

$2n$

Correct Answer:

$2^n$

Explanation:

$A^n=A×A×A.......A$

So $|A^n|=|A×A×A.......A|$

$=|A|×|A|×|A|....|A|$

$=|A|^n=2^n$