Dear student XA=BXAA-1=BA-1X=BA-1 (1)Now A=101023121A=101023121=12-6-0+10-2=-4+0-2=-6Now, we will calculate co-factorsC11=1C12=0C13=1C21=0C22=2C23=3C31=1C32=2C33=1AdjA=101023121T=101022131A-1=1AadjA=-16101022131Now, Consider eq(1), we haveX=BA-1=-16123115247101022131=-164138617892917=-23-136-43-1-176-43-32-296-176 Regards

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find matrix

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XA = B {XAA}^{- 1} = {BA}^{- 1} X = {BA}^{- 1} . . . (1) Now A = [\begin{matrix} 1 & 0 & 1 \\ 0 & 2 & 3 \\ 1 & 2 & 1 \end{matrix}] |A| = |\begin{matrix} 1 & 0 & 1 \\ 0 & 2 & 3 \\ 1 & 2 & 1 \end{matrix}| = 1 (2 - 6) - 0 + 1 (0 - 2) = - 4 + 0 - 2 = - 6 Now, we will calculate co - factors C_{11} = 1 C_{12} = 0 C_{13} = 1 C_{21} = 0 C_{22} = 2 C_{23} = 3 C_{31} = 1 C_{32} = 2 C_{33} = 1 AdjA = {[\begin{matrix} 1 & 0 & 1 \\ 0 & 2 & 3 \\ 1 & 2 & 1 \end{matrix}]}^{T} = [\begin{matrix} 1 & 0 & 1 \\ 0 & 2 & 2 \\ 1 & 3 & 1 \end{matrix}] A^{- 1} = \frac{1}{|A|} adjA = \frac{- 1}{6} [\begin{matrix} 1 & 0 & 1 \\ 0 & 2 & 2 \\ 1 & 3 & 1 \end{matrix}] Now, Consider eq (1), we have X = {BA}^{- 1} = \frac{- 1}{6} [\begin{matrix} 1 & 2 & 3 \\ 1 & 1 & 5 \\ 2 & 4 & 7 \end{matrix}] [\begin{matrix} 1 & 0 & 1 \\ 0 & 2 & 2 \\ 1 & 3 & 1 \end{matrix}] = \frac{- 1}{6} [\begin{matrix} 4 & 13 & 8 \\ 6 & 17 & 8 \\ 9 & 29 & 17 \end{matrix}] = [\begin{matrix} \frac{- 2}{3} & \frac{- 13}{6} & - \frac{4}{3} \\ - 1 & \frac{- 17}{6} & \frac{- 4}{3} \\ - \frac{3}{2} & - \frac{29}{6} & \frac{- 17}{6} \end{matrix}]

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