Properties of DeterminantsState the appropriate theorems that justifies the given equality, with solution. 3. State the32265 - 8appropriate theorems that justifies the given equality.13- 4= 0 There are properties of determinants to simplify its computation.Theorem: Determinant of a TransposeIf AT is the transpose of the n x n matrix A, then det AT = det A.Theorem: Two Identical RowsIf any two rows (columns) of an n x n matrix A are the same, then det A = 0.Theorem: Zero Row or ColumnIf all the entries in a row (column) of an n x n matrix A are zero, then det A = 0.Theorem: Interchanging RowsIf B is the matrix obtained by interchanging any two rows (columns) of an n x n matrix A, then det B = -det A.Theorem: Constant Multiple of a RowIf B is the matrix obtained from an n x n matrix A by multiplying a row (column) by a non zero real number k, then det B = k det A.Theorem: Determinant of a Matrix ProductIf A and B are both n x n matrices, then det AB = det A x det BTheorem: Determinant is unchangedIf matrix B is obtained from multiplying entries from row(column) and adding corresponding entries to another row then the det B = det A.Theorem: Determinant of a triangular matrixIf matrix A is an n x n triangular matrix (upper or lower). Then det A = a₁1₁a22...ann where a11a22...ann are the entries on the main diagonal of A.Theorem: A Property of CofactorsSuppose A is an n x n matrix. If we get the cofactors of the entries in the kth row.When we obtain the cofactor for the jth columna₁1Ck1 + a2Ck2 +...+ ainCkn = 0, for i #ka1jC1k + a2jC2k +...+ anjCnk = 0, for j #k

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To state the theorem for the given equality

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3. State the 3 2 2 6 5-8 8-4 appropriate theorems that justifies the given equality. 1 3 0