Let A= pmatrix 1 10& 3 10\ -3 10& 1 10 pmatrix and B= pmatrix1&-i\0&1 pmatrix, where i= -1. If M=A^TBA, then the inverse of the matrix AM^2023A^T is

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Correct answer: D. (d) Solution AA^T= ( 1 10 3 10 -3 10 1 10 ) ( 1 10 -3 10 3 10 1 10 )- (1001 ) B^2=(1-i01)(1-i01)=(1-2i01) B=(1-3i01 ) B^2023=(1-2023i01) M=A^1 BA M^2=M .M=A^2 BAA^1 BA=A^2B^2A M^3=M^2M=A^2B^2AA^1 BA=A^2B^2A M^2023=.................. A^1B^2033A AM^2023A^T=AA^T B^1012AA^T=B^2023 =( 1-2023i01) Inverse of (AM^2023 A^T ) is (12023i01 )

$Let A = (\frac{1}{10} \frac{- 3}{10} \frac{3}{10} \frac{1}{10}) and B = (10 - i 1), where i = - 1 . If M = A^{T} B A, then the inverse of the matrix A M^{2023} A^{T} is$

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