matrix prove?

Question

show by means of an example that det(A+B) notequal to detA+detB
please shoe mw work thanks in advance

Answer 1

Let A =
[1 -1]
[1 1]

B =
[-1 1]
[-1 -1]

Notice that detA = 1 - (-1) = 2
detB = 1 - (-1) = 2

But A + B =
[0 0]
[0 0]

So det(A) + det(B) = 4, but
det(A + B) = 0