Two 3 × 3 matrices A and B are related by A = 2B, what is the relation between Det(A) and Det(B)?

Answer 1

The determinant is a multi-linear function on the rows of a matrix. That means, in particular, that if a row of a matrix is multiplied by some number (scalar), the determinant of this new matrix is that number multiplied by the determinant of the old matrix.

If we multiply a whole matrix by a number r, this is equivalent to multiplying all the rows by r, so the new determinant is r^(# of rows) multiplied by the old determinant. In simple math terms,

det(A)= det(2B) = 2^3 det(B) = 8 det(B).