Recall that the function f:X to Y is invertible with inverse function g: Y to X if g(f(x))=x for all x in X and f(g(x))=x for all x in Y. Suppose T: R^n to^n is a matrix transformation defined by T(x)=A(x). Prove that if A is an invertible matrix then T is an invertible function.    Hint: Can you think of another matrix transformation that acts as the inverse for T?

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Q: 1. The trace of a matrix is defined to be the sum of its diagonal matrix elements Tr(Ω) = ΣΩ Show…

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