Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows that the statement is not true in all cases or cite an appropriate statement from the text. (a) The determinant of the sum of two matrices equals the sum of the determinants of the matrices. O False, consider the following matrices: [ 7 2 ] and [ => > ]- True, the determinant of the sum of an even number of matrices is equal to the sum of the determinants of those matrices. True, the determinant of the sum of any number of matrices equals the sum of the determinants of those matrices. O False, consider the following matrices: [ ? $ ] and [ 3 $ ]. O False, consider the following matrices: g 8 and [ : 8 ]. (b) If A and B are square matrices of order n, and det(A) = det(B), then det(AB) = det(A2). O True, using the given the conditions det(AB) = det(A) det(B) = det(A)det(-A) = det(A(-A)) = det(A2). O False, using the given the conditions det(AB) = det(A)det(B) = det(A) + det(A) = 2det(A) = det(2A). O True, using the given the conditions det(AB) = det(A)det(B) = det(A)det(A) = det(AA) = det(A2). O True, using the given the conditions det(AB) = det(A)det(B) = det(A) + det(A) = 2det(A) = det(A2). O False, using the given the conditions det(AB) = det(A) det(B) = det(A)det(A) = det(2A). (c) If the determinant of an n x n matrix A is nonzero, then Ax = O has only the trivial solution. O False, if the determinant of an n x n matrix A is nonzero then the matrix is not invertible, which means that Ax = O has no solutions. O True, if the determinant of an n x n matrix A is nonzero then the matrix is invertible, which means that Ax = O has only the trivial solution. O False, if the determinant of an n x n matrix A is nonzero then the matrix is invertible, which means that Ax = O has infinite solutions. O True, if the determinant of an n x n matrix A is nonzero then the matrix is not invertible, which means that Ax = O has only the trivial solution. O False, if the determinant of an n x n matrix A is nonzero then the matrix is not invertible, which means that Ax = O has infinite solutions. Need Help? Read It