The inverse of a diagonal non-singular matrix | vedclass

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Question

(D) Let $A$ be a diagonal matrix of order $n 	imes n$ defined as $A = 	ext{diag}(a_1, a_2, \dots, a_n)$,where $a_i 
eq 0$ for all $i$ because the m

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diagonal matrix

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(D) Let $A$ be a diagonal matrix of order $n 	imes n$ defined as $A = 	ext{diag}(a_1, a_2, \dots, a_n)$,where $a_i 
eq 0$ for all $i$ because the matrix is non-singular. The inverse of a diagonal matrix $A$ is given by $A^{-1} = 	ext{diag}(1/a_1, 1/a_2, \dots, 1/a_n)$. Since all off-diagonal elements of $A^{-1}$ remain $0$,the resulting matrix $A^{-1}$ is also a diagonal matrix. Thus,the inverse of a diagonal non-singular matrix is a diagonal matrix.

The inverse of a diagonal non-singular matrix is:

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