# if a and b are any two matrices, then

It only takes a minute to sign up. Let A and B be two matrices such that A = 0, AB = 0, then equation always implies that 58. If A is any matrix and α∈F then the scalar multipli-cation B = αA is deﬁned by b ij = αa ij all i,j. Circulant matrices commute. If A is a 3 x 3 matrix and det (3A) = k { det (A)}, then … If A and B are symmetric matrices then AB+BA is a symmetric matrix (thus symmetric matrices form a so-called Jordan algebra). If A and B are two non-singular square matrices of the same order, the adjoint of AB is equal to (A) (adj A) (adj B) (B) (adj B) (adj A) asked Dec 6, 2019 in Trigonometry by Vikky01 ( 41.7k points) matrices The sum of two symmetric matrices is a symmetric matrix. It's the same with matrices - if the dot product is zero, then they are orthogonal (perpendicular). If you have two vectors that are orthogonal, their dot product is zero - for example <0,1> times <1,0> = <0,0>. The proof of Theorem 2. Deﬁnition 2.1.4. In linear algebra, two n-by-n matrices A and B are called similar if there exists an invertible n-by-n matrix P such that = −. How to Determine if a Matrix is Invertible (d) A 3×m and B 3×n are two matrices . Deﬁnition 2.1.5. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Every diagonal matrix commutes with all other diagonal matrices. They form a commutative ring since the sum of two circulant matrices is circulant. If A is an orthogonal matrix, then 59. If we multiply a symmetric matrix by a scalar, the result will be a symmetric matrix. Matrix theory was introduced by 60. Theorem 2: A square matrix is invertible if and only if its determinant is non-zero. In such a case matrix B is known as the inverse of matrix A. Inverse of matrix A is symbolically represented by 'A-1 '. Two of the most important theorems about determinants are yet to be proved: Theorem 1: If A and B are both n n matrices, then detAdetB = det(AB). If m = n, then A and B have same orders as 3×n each, so the order of (5A-2B) should be same as 3×n. If multiplying A^2, then it's asking you to multiply the identity matrix by itself, giving you the identity matrix. Jordan blocks commute with upper triangular matrices that have the same value along bands. Two matrices A and B are equal if and only if they have thesamesizeand a ij = b ij all i,j. If the product of two symmetric matrices is symmetric, then they must commute. A. For example, if matrix A and B satisfy this condition AB=BA=I, then we can say B is the inverse of A written as A-1 =B. If A is a skew-symmetric matrix, then trace of A is (a)-5 (b) 0 (c) 24 (d) 9 61. 1. If a and B Are Square Matrices of the Same Order, Then (A + B)(A − B) is Equal to - Mathematics. If A and B are square matrices of the same order, then (A + B)(A − B) is equal to . If you graph these two vectors, you can see that one's on the y axis and one's on the x. Question By default show hide Solutions. Similarly, we can also say A is the inverse of B written as B-1. Options A 2 − B 2 A 2 − BA − AB − B 2. Use the multiplicative property of determinants (Theorem 1) to give a one line proof If A and B are matrices of the same size then the sum The answer is only A+B because when multiplying the identity matrix with any other matrix, the same numbers in the matrix that isn't the identity matrix will be unchanged and the answer.