If B is a non-singular 4 x 4 matrix and A is its adjoint such that |A| = 125, then |B| is

The correct option is 5.

To understand why this is correct, we can use the properties of determinants and adjoint matrices.

For any square matrix $B$ of order $n$, the determinant of its adjoint matrix, denoted by $A=\text{adj}\left(B\right)$, is given by the formula:
$\left|\text{adj}\right(B\left)\right|={\left|B\right|}^{n-1}$

Here, we are given:
1. $B$ is a non-singular $4\times 4$ matrix, which means its order is $n=4$.
2. The adjoint of $B$ is $A$, so $A=\text{adj}\left(B\right)$.
3. The determinant of $A$ is $\left|A\right|=125$.

Substituting $n=4$ and $\left|\text{adj}\right(B\left)\right|=\left|A\right|=125$ into the formula, we get:
$125={\left|B\right|}^{4-1}$

Simplifying the exponent:
$125={\left|B\right|}^3$

Since we know that $5^3=125$, taking the cube root on both sides gives:
$\left|B\right|=5$

Therefore, the determinant of matrix $B$ is 5.