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12 Nov 2019
(d) (i) Prove if A is invertible, then A^T is invertible and (A^T)^-1 = (A^-1)^T. (ii) Prove if A and B are both invertible then so is AB and (AB)^-1 = B^-1A^-1. (iii) A square matrix is called skew-symmetric if A^T = -A. Prove that if A and B are skew-symmetric matrices, then A + B is skew-symmetric.
(d) (i) Prove if A is invertible, then A^T is invertible and (A^T)^-1 = (A^-1)^T. (ii) Prove if A and B are both invertible then so is AB and (AB)^-1 = B^-1A^-1. (iii) A square matrix is called skew-symmetric if A^T = -A. Prove that if A and B are skew-symmetric matrices, then A + B is skew-symmetric.
Elin HesselLv2
9 Sep 2019