Indicate whether the statements is always true or sometimes false. Justify each iswer by given either a proof, a logical argument, or a counter example. a) If A is a symmetric matrix, then A? – A is symmetric. b) If A, B, and C are square matrices of the same size such that AC = BC, then A = B. c) If A is an n x n matrix and k is a scalar, then Tr(kA) = kTr(A). d) For any n xn matrix A, (kA)² = k² A²

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.