If A = [(3 -2), (4 -2)], find the value of λ so that A^2 = λA – 2I. Hence, find A^–1.

Question

If \(A=\begin{bmatrix}3&-2\\4&-2\end{bmatrix}\), find the value of λ so that A² = λA – 2I. 

Hence, find A^–1.

Answer 1

\(A=\begin{bmatrix}3&-2\\4&-2\end{bmatrix}\)

A² =\(\begin{bmatrix}3&-2\\4&-2\end{bmatrix}\)\(\begin{bmatrix}3&-2\\4&-2\end{bmatrix}\)\(=\begin{bmatrix}9-8&-6+4\\12-8&-8+4\end{bmatrix}\)

\(=\begin{bmatrix}1&-2\\4&-4\end{bmatrix}\)

Now, A² = λA – 2I

= λA = A² + 2I