Answer each of the following either "TRUE" or “FALSE".If you answer "TRUE", give an explanation why it's true; if you answer "FALSE", either give an explanationor give an example that demonstrates why it's false.(a) If A is a square matrix with det(A) = 0, then A is not invertible.(b) For any compatible square matrices A and B, det(A+ B) = det(A) + det(B).(c) In R², the set of vectorswith x <0 and y <0 is a subspace.а(d) For a 3 x 3 matrix A, det(r A) = r³ det(A).(e) Every change of basis matrix Pc-B is invertible.

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"TRUE", give an explanation why it's true; if you answer “FALSE", either give an explar or give an example that demonstrates why it's false. (a) If A is a square matrix with det(A³) = 0, then A is not invertible. (b) For any compatible square matrices A and B, det(A+ B) = det(A) + det(B). (c) In R², the set of vectors with x <0 and y < 0 is a subspace. (d) For a 3 x 3 matrix A, det (rA) = r³ det(A). (e) Every change of basis matrix Pc-B is invertible.