Witryna5. [0 b a 0]4 = I, then. 6. If x[−3 4] +y[4 3] = [10 −5], then. 7. If A and B are square matrices of the same order and if A = AT,B = B T, then (AB A)T =. 8. If A = [3 1 −4 −1], then (A −A′) is equal to (where, A′ is transpose of matrix A ) 9. Let A be a square matrix and AT is its transpose, then A + AT is. Witryna1. If A and B are two square matrices of same order, then (A + B) (A − B) = A 2 − B 2. 2. If A and B are two square matrices of same order, then (A B) n = A n B n. 3. If A and B are two matrices such that A B = A and B A = B, then A and B are idempotent. Which of these is/are not correct?
matrices - When will $AB=BA$? - Mathematics Stack Exchange
WitrynaIf A and B are square matrices such that AB=I and BA=I, then B is A Unit matrix B Null matrix C Multiplicative inverse matrix of A D −A Easy Solution Verified by Toppr Correct option is C) AB=I & BA=I then B is the multiplicative inverse of A. Hence, the answer is multiplicative inverse matrix of A. Solve any question of Matrices with:- WitrynaIf A and B are symmetric matrices of the same order and X=AB+BA and Y =AB−BA, then XY T is equal to. If A, B are symmetric matrices of same order then the matrix AB-BA is a. Q. If A and B are symmetric matrices of same order, prove that AB- BA is … relax everyday with linh mun
Properties of matrix operations - Massachusetts Institute of …
Witryna12 wrz 2024 · Since the matrix product AB is defined, we must have n = r and the size of AB is m × s. Since AB is a square matrix, we have m = s. Thus the size of the matrix B is n × m. From this, we see that the product BA is defined and its size is n × n, hence it is a square matrix. Click here if solved 120 Tweet Add to solve later Sponsored Links × A Witryna4 mar 2024 · 1 Answer Ratnaker Mehta Mar 4, 2024 Kindly refer to the Explanation. Explanation: Since A and B are square matrices, all the multiplications reqd. in the Question are defined. Now, (A +B)2 = (A+ B) ⋅ (A +B), = A(A+ B) +B(A+ B), = A ⋅ A+ A⋅ B + B ⋅ A +B ⋅ B, = A2 + A⋅ B +A ⋅ B +B2 .......[ ∵,A ⋅ B = B ⋅ A, Given], = A2 + 2A⋅ B + B2,i.e., WitrynaIf A and B are two matrices such that AB=BA, then for every `n epsilonN` (A) `(AB)^n=A^nB^n` (B) `A^nB=BA^n` (C) `(A^(2n)-B^(2n))=(A^n-B^n)(A^n+B^n)` (D) `(A... product of diagonal matrices