Let $A = \begin{pmatrix} 2 & k \ 5 & 3 \end{pmatrix}$. It is known that the inverse of $A$ exists and that the sum of the elements of $A^{-1}$ equals 1. Find the value of $k$ and then compute the determinant of the matrix $B = A^{2} - 4A$.

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Accepted Answer

k = \frac{3}{2}, \; \det(B)=\frac{33}{4}

Neco 2021 Further Mathematics Question 1

Let \(A = \begin{pmatrix} 2 & k \\ 5 & 3 \end{pmatrix}\). It is known that the inverse of \(A\) exists and that the sum of the elements of \(A^{-1}\) equals 1. Find the value of \(k\) and then compute the determinant of the matrix \(B = A^{2} - 4A\).

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