If the determinant of a 55 matrix A is detA4 and the matrix

If the determinant of a 5×5 matrix A is det(A)=4, and the matrix D is obtained from A by adding 5 times the fourth row to the second, then det(D) =

Solution

Some row operations for determinant of matrix are as follows:

Adding a multiple of one row to another no change to determinant
swapping rows changes the sign ( + / - ) of determinant
Multiplying a row by a scalar multiplies determinant by that scalar

Here matrix D is obtained from A by adding 5 times the fourth row to the second.

hence Adding a multiple of one row to another no change to determinant

then det(D) = 4.