Question

WILL GIVE BRAINLIEST AND 25 POINTS! Which of the following statements are true? Check all that apply. A. If any row of a square matrix is zero, its determinant is zero. B. If all numbers in a matrix are equal, its determinant is zero. C. The determinant of any identity matrix is zero. D. The determinant of a matrix with all positive numbers is always positive. E. The determinant of any zero matrix is zero.

Answer 1

Answer:

Option A, B and E

Step-by-step explanation:

Determinant = ad-bc

Let's look at the picture and solve all

Option A)

If the row ( c and d ) is zero, the determinant will be zero

=> a(0)-b(0)

=> 0-0

=> 0 (So, True)

Option B)

If a = b = c = d (Let's say 1), the determinant will be

=> (1)(1)-(1)(1)

=> 1-1

=> 0  (So, True)

Option C)

An Identity matrix is

=> $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

So , it's determinant will be

=> (1)(1)-(0)(0)

=> 1-0

=> 1  (So, False)

Option D)

The determinant with matrix will all positive numbers can be negative as well as positive. This is not necessary that it would be positive. (So, False)

Option E)

A zero matrix is

=> $\left[\begin{array}{ccc}0&0\\0&0\end{array}\right]$

So, it's determinant is:

=> (0)(0)-(0)(0)

=> 0-0

=> 0 (So,True)