Suppose A and B are matrices such that the product C = AB is defined. Using the result rank ( C ) <= min { rank(A), rank(B) } , prove that rank (A^2) <= rank (A) , where A is a squre matrix.
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In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing another matrix, often denoted by AT (among other notations).
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