For each of the following, determine if the statement is true or false. Provide a short reasoning (one or two sentences). a) Let A be an n xn matrix, and b be a vector in R". If the system A = 5 has infinitely many solutions, then A is not invertible. b) Let A be an invertible square matrix. If AB = AC, then B = C. c) If A and B are square matrices such that AB = BA, then A-1 = B. d) Let A be n x m, B be px n, C be l x k and D be px k. Then (CD"BA)" is m x l. e) Let T be an invertible linear transformation. If T() = 0, then = 0.

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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.