If k>1 and the determinant of the matrix A^2 , where A= [ array ccc k & k & 0 & & k 0 & 0 & k array ] , is k^2 , then | | equal to

Step-by-step solution

aligned & Given A= [ array rrr k & k & 0 & & k 0 & 0 & k array ] & |A|= k^2 & Now aligned |A^2 | & =|A|^2 & = ( k^2 )^2 & = ^2 k^4 aligned aligned According to given condition, array rlrl & & |A^2 | & =k^2 & & ^4 k^4 & =k^2 & ^4 & = 1 k^2 & & & = 1 k array