Question

Find the inverse of each of the matrices(if it exists). \(\begin{bmatrix}-1&5\\-3&2\end{bmatrix}\)

Answer 1

Let A=\(\begin{bmatrix}-1&5\\-3&2\end{bmatrix}\)

IAI=-2+15=13
Now A₁₁=2 ,A₁₂=3, A₂₁=-5, A₂₂=-1
therefore adj A=\(\begin{bmatrix}2&-5\\3&1\end{bmatrix}\)

therefore A^-1=\(\frac{1}{\mid A\mid}\)adj A=\(\frac{1}{13}\) \(\begin{bmatrix}2&-5\\3&1\end{bmatrix}\)