[quad A=[[a,0,1],[0,b,2],[-1,0,c]]" ,where "a,b,c" are "],[" Let "],[" positive integers.If "tr(A)=7" then "],[" greatest value of "|A|],[" (Note "tr(A)" denotes trace of matrix) "]

Let A=[(1,0,3),(0,b,5),(-(1)/(3),0,c)] , where a, b, c are positive integers. If tr(A)=7 , then the greatest value of |A| is (where tr (A) denotes the trace of matric A i.e. the sum of principal diagonal elements of matrix A)

[A=[[a,b,c],[b,c,a],[c,a,b]]" ,If trace "(A)=9," and "a,b,c" are "],[" positive integers such that "ab+bc+ca=26." Let "],[A," denote the adjoint of matrix "A_(1),A_(2)" represent "],[" adjoint of "A_(1)...." and so on,if value of "det(A_(4))" is "],[M" then "]

If the matrix {:[(a+b,0,0),(0,b+c,0),(0,0,c+a)]:} , (where a,b,c are positive integers) is a scalar matrix, then the value of (a+b+c) can be

Let Z=[(1,1,3),(5,1,2),(3,1,0)] and P=[(1,0,2),(2,1,0),(3,0,1)] . If Z=PQ^(-1) , where Q is a square matrix of order 3, then the value of Tr((adjQ)P) is equal to (where Tr(A) represents the trace of a matrix A i.e. the sum of all the diagonal elements of the matrix A and adjB represents the adjoint matrix of matrix B)

Let M=[[a,-360],[b,c]], where a,b and c are integers.Find the smallest positive value of b such that M^(2)=0 , where O denotes 2times2 null matrix.

Let A=[a_(ij)] be a matrix of order 3 such that AP=2I where "I" is an identity matrix of order 3 and qquad P=[[1,2,3],[0,1,4],[0,0,1]]. Identify which of the following statement (s) is (are) correct? [ Note: adj.(M) denotes adjoint matrix of matrix ,M and Tr.(M) denotes trace of matrix M.]

If a+b+c=3 and a>0,b>0,c>0 the greatest value of a^(2)b^(3)c^(2)

[" Consider the system "AX=B" ,where "A=[[1,1,-1],[2,1,1],[3,2,2]],X=[[x],[y],[z]],B=[[-1],[2],[3]]],[" Value of tr "(XB^(TT))" is (where "tr(A)" denotes trace of matrix "A)],[[" (a) "0," (b) "1," (c) "2," (d) "3]]

If A=[[-1,10,-2]]=B^(3)+C^(3), where B and c are 2x2 matrices with integer elements, then- tr(B)-tr(C) must be equal to