Chapter 6, Problem 1E

If B is obtained be multiplying a column of A by 9, then the equation $\det B=9\det A$ must hold.

To determine

If the given statement is true or false.

Answer to Problem 1E

True.

Explanation of Solution

Given information:

An statement is given as -

If $B$ is obtained be multiplying a column of $A\text{ by 9}$ , then the equation $\det B=9\det A$ must hold.

Calculation:

Using the properties of determinant -

If $B$ is obtained be multiplying a column of $A$ by a scalar $k$ , then

  $\det B=k\det A$ .

So, when column of $A$ is multiplied by $9$ then, the equation $\det B=9\det A$ must hold.

Hence, the given statement is true.