Let matrix A = `[[1,0,0],[25,1,0],[25,0,1]]` and a matrix B of third order with its columns as `B_1`,`B_2`,`B_3` be such that `AB_1`=`[[1],[25],[25]]`, `AB_2` = `[[0],[1],[0]]`, and `AB_3` = `[[0],[0],[1]]`. Find `det(adj B)`.

If A=[[1,0,0],[0,1,0],[a,b,-1]] , find A^2

If A=[[2,1],[3,0],[5,1]] and B = [[4,0],[3,8]] then find AB

If A=[[2,1,3],[4,1,0]] and B=[[1,-1],[0,2],[5,0]] find AB and BA.

Let A = [[1,0,0],[1,0,1], [0,1,0]] " satisfies " A^(n) = A^(n-2) + A^(2 ) -I for nge 3 and consider matrix underset(3xx3)(U) with its columns as U_(1), U_(2), U_(3), such that A^(50)U_(1)=[[1],[25],[25]],A^(50) U_(2)=[[0],[1],[0]]and A^(50) U_(3)[[0],[0],[1]] The value of abs(A^(50)) equals

Let A= [[1,0,0],[2,1,0],[3,2,1]] be a square matrix and C_(1), C_(2), C_(3) be three column matrices satisfying AC_(1) = [[1],[0],[0]], AC_(2) = [[2],[3],[0]] and AC_(3)= [[2],[3],[1]] of matrix B. If the matrix C= 1/3 (AcdotB). The ratio of the trace of the matrix B to the matrix C, is

Let A= [[1,0,0],[2,1,0],[3,2,1]] be a square matrix and C_(1), C_(2), C_(3) be three comumn matrices satisfying AC_(1) = [[1],[0],[0]], AC_(2) = [[2],[3],[0]] and AC_(3)= [[2],[3],[1]] of matrix B. If the matrix C= 1/3 (AcdotB). The value of det(B^(-1)) , is

Find AB, if A=[[0,-1],[ 0, 2]] and B=[[3, 5],[ 0, 0]] .

Let A= [[1,0,0],[2,1,0],[3,2,1]] be a square matrix and C_(1), C_(2), C_(3) be three comumn matrices satisgying AC_(1) = [[1],[0],[0]], AC_(2) = [[2],[3],[0]] and AC_(3)= [[2],[3],[1]] of matrix B. If the matrix C= 1/3 (AcdotB). find sin^(-1) (detA) + tan^(-1) (9det C)

If A=[[10,3],[1,2]] and B=[[1,0],[1,-1]] , verify that (AB)\'=B\'A\'