if I have a Scalar Matrix A then in inverse is it the same as Matrix A transpose $(kA)^{-1} = A^T $ How can I prove this property? I would appreciate it if somebody can help me.
2026-03-26 06:30:58.1774506658
Proof: The scalar of the inverse matrix is the matrix transpose.
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For scalar $A, k$ you have $A^T = A$ and $(k A)^{-1} = 1/(k A)$ so just solve $A = 1/(k A)$ for $k$ you get $k = 1/A$. Of course this is only valid for $k A \neq 0$.