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Problem 1. 15pts.Determine whether the following statements are true or false. If the statement is...

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Problem 1. 15pts.Determine whether the following statements are true or false. If the statement is true,write T in the box provided under the statement. If the statement is false, write F inthe box provided under the statement. Do not write "true" or "false".(a)If A and B are symmetric n x n matrices, then ABBA must be symmetric aswell.If A is an invertible matrix such that A- = A, then A must be orthogonal.If V is a subspace of R" and is a vector in R", then the inequality (proj) 20 must hold.(d)(b)(e)-If matrix B is obtained by swapping two rows of an n x n matrix A, then theequation det (B) = -det (4) must hold.There exist real invertible 3 x 3 matrices A and S such that ST AS = -A.

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