Answer #1 subpart d I Solve the following problems. Show your detailed solution.1. Prove that the properties of determinants are true by solving the following[-1 -4 431 -5-5A =2 3 -5 B1 =5 -4 4 3-6 5-4 -31-36-14B2 =-7 -44-6 -616-3 -21-634-4 -3)-3[-2 -4D=1 23.3 6 -21l-6C=1 73 4k= -2Answera Using Matrix [A] prove that the Property 1 and 2 of determinant are true.b. Using Matrix [C] and k prove that Property 3 of determinant is true.C Using Matrix [Dj prove that Property 4 of determinant is true.d. Using Matrix [81] and (B2) prove that by solving the determinant of these matricesseparately and getting its sum will give the same answer with the use of Property 5.NOTE Use your convenient method when solving the determinant of the given matrices PROPERTIES OF DETERMINANTS1. Determinant of a TransposeThe determinant of a transpose A" of A is equal to the determinart of A.det(A") = det(A)2. Interchange of Rows and ColumnsThe determinant changes its sign if two adjacent rows (or columns) are interchanged.E:9-Eja21 az2a1 a12*** aznainaina21Jani an2annlJant anzan3. Multiplication of a determinant by a Numberk det(A) = det(A')Where:The matrix A' differs from A in that any one of its row or columns is multiplied by k.PROPERTIES OF DETERMINANTS4. Determinant with equal rows or columns- The determinant of A is zero if two of its rows or columns are proportional to each otherelement by element.- The determinant of A is zero if two rows or columns are equal.- The determinant of A is zero if a row or column has only null elements.5. Sum of DeterminantsConsider matrix A = [a,] and matrix A', with all elements equal to A except for one row or column:[an a12aa12ainaz1 a2A =A' =...ajzba babThen: det(A) + det(A') =au + bu aa + b2an + binainlani anzLant an2annantan2ann

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I Solve the following problems. Show your detailed solution. 1. Prove that the properties of determinants are true by solving the following: 3 1 -5 01 5 -4 4 3 --5 -1 -4 4 A = 2 3 -5 B1 = 6 -3 -4 4 3 B2 = -3 -6 -6 -6 -6 5 4 -2 -4 --6 k= -2 1 7 -1 1 2 Answer 6. -21 a Using Matrix [A] prove that the Property 1 and 2 of determinant are true. b. Using Matrix C] and k prove that Property 3 of determinant is true. c Using Matrix Dj prove that Property 4 of determinant is true. d. Using Matrix [B1] and [B2) prove that by solving the determinant of these matrices separately and getting its sum will give the same answer with the use of Property 5. NOTE: Use your covenient method when solving the determinant of the given matrices