detA B detA detBSolutionNo this is false statement We tak

det(A + B) = det(A) + det(B).

Solution

No, this is false statement. We take a counter example to get it. LEt us consider two diagnonal matrices P and Q such that
P= Ip1, .0.|
.....I .0.,p2|

and

Q= I q1 .0.|
. ...I .0., q2|

then det(P) = p1p2.
det(Q) = q1q2

or det(P) + det (Q)= p1p2 + q1q2
but det(P+Q) = (p1+q1) * (p2 +q2) = p1p2 + q1q2+ p1q2 + q1p2.

so det(P+Q) is not equal to det(P) + det (Q)