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Mathematics Question on Determinants

Find the inverse of each of the matrices(if it exists). [−15−32]\begin{bmatrix}-1&5\\\\-3&2\end{bmatrix}

Answer

Let A=[−15−32]\begin{bmatrix}-1&5\\\\-3&2\end{bmatrix}

IAI=-2+15=13
Now A11=2 ,A12=3, A21=-5, A22=-1
therefore adj A=[2−5\31]\begin{bmatrix}2&-5\\\3&1\end{bmatrix}

therefore A-1=1∣A∣\frac{1}{\mid A\mid}adj A=113\frac{1}{13} [2−5\31]\begin{bmatrix}2&-5\\\3&1\end{bmatrix}