Question

Two matrices, $ A $ and $ B $ are both $ 5 \times 5 $ square matrices such that $ A = kB $ , where $ k $ is a non zero constant. If $ |B| = z $ , then what will be the value of $ |4(A + B)| $ ?

• A. $ 5z $
• B. $ (20k + 20)z $
• C. $ 3125z $
• D. $ (4k + 4)^5z $

Answer 1

Answer: (D)

We are given that,
$A = kB \,\,\,...(i)$
and $|B| = z \,\,\,...(ii)$
Now, $|4(A + B)| = |4(kB + B)|$ (using $(i)$)
$= |4(k + 1)B| = (4k + 4)^5|B|$
$ = (4k + 4)^2z$ (using $(ii)$)