If A and B are matrices of order 4 x 4 such that A= 5B and determinant of A = X. (determinant of B), then X will be

Question

If $A$ and $B$ are matrices of order $4 \times 4$ such that $A= 5B$ and determinant of $A = X$. (determinant of $B$), then $X$ will be

• A. $5$
• B. $25$
• C. $125$
• D. $625$

Answer 1

|A|=X.|B|

As given A =5B ,TAKING determinant of both side

|A| =|5B|

  |A|=$5^4$|B| (Property of determinant ,|kA|=$k^n$|A|,where n is order of det.)

So X=625