If (A= [ array ccc 1 & 0 & -2 -2 & -1 & 2 3 & 4 & 1 array ] ), then (A⁻¹= )

Step-by-step solution

Characteristic equation of any square matrix (A ) is given by ( aligned & |A- I|=0 & [ array ccc 1 & 0 & -2 -2 & -1 & 2 3 & 4 & 1 array ]- [ array lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ]=0 & [ array ccc 1 & 0 & -2 -2 & -1 & 2 3 & 4 & 1 array ]- [ array ccc & 0 & 0 0 & & 0 0 & 0 & array ]=0 & | array ccc 1- & 0 & -2 -2 & -1- & 2 3 & 4 & 1- array |=0 & (1- )[-(1+ )(1- )-8]-2[-8+3( +1)]=0 & (1- ) [- (1- ^2 )-8 ]-2(-8+3 +3)=0 & (1- ) ( ^2-9 )-2(-5+3 )=0 & ^2-9- ^3+9 -6 +10=0 & - ^3+ ^2+3 +1=0 & ^3- ^2-3 -1=0 aligned