Matrix Transformation

Step 1: Analyze the Given Information

We are given that . Taking the determinant of both sides:

Since , we have:

We are also given that .

Step 2: Analyze B

To continue, we must know something that holds true for Matrix B. Let's add information into the equation such as |A|= 1 the |B|=-1 and say that Then the new equation of A+B=0

Step 3: Analyze A + B, if |A|= 1 the |B|=-1 and |A+B|=0

Add these equation together for the total value, then |A+B|=0 Then A+B is Singular, and can hold true

Conclusion:

Given |A|= 1 the |B|=-1 and |A+B|=0 : A+B is singular.