Question

If $A=kB$, where $A$ and $B$ are square matrices of order $n$, then for $n=1,2,3$,

• A. $|A|=k|B|$
• B. $|A|=nk|B|$
• C. $|A|=n+k|B|$
• D. $|A|=k^n|B|$

Answer 1

Answer: (D)

In general, if $A=kB$, where $A$ and $B$ are square matrices of order $n$, then $|A|=k^n|B|$, where $n=1,2,3$.