If A is a square matrix such that $|A|= 2$, then for any positive integer n, $|A^n|$ is equal to
Answer & explanation
Correct answer: option 1
$A^n=A×A×A.......A$
So $|A^n|=|A×A×A.......A|$
$=|A|×|A|×|A|....|A|$
$=|A|^n=2^n$
If A is a square matrix such that $|A|= 2$, then for any positive integer n, $|A^n|$ is equal to
Correct answer: option 1
$A^n=A×A×A.......A$
So $|A^n|=|A×A×A.......A|$
$=|A|×|A|×|A|....|A|$
$=|A|^n=2^n$