Matrix `M_(r)` is defined as `M_(r)`=\begin{bmatrix}r & r-1\\r-1 & r\end{bmatrix} , `r in N`; value of `det(M_(1))+det(M_(2))+det(M_(3))+...+det(M_(2007))` is

If A is a 3 × 3 invertible matrix, then what will be the value of k if det(A^(–1)) = (det A)^k .

If A is an invertible matrix of order 2, then det (A^(-1)) is equal to (A) det (A) (B) 1/(det(A) (C) 1 (D) 0

If A is an invertible matrix of order 2, then det (A^(-1)) is equal to(a) det (A) (B) 1/(det(A) (C) 1 (D) 0

Let A be a square matrix of order 3 such that det. (A)=1/3 , then the value of det. ("adj. "A^(-1)) is

Let M = [a_(ij)]_(3xx3) where a_(ij) in {-1,1} . Find the maximum possible value of det(M).

If A is an invertble matrix of order 2 then (det A ^-1) is equal to- a.det A b.1/ det A c. 1 d. 0

Consider two solid sphere of radii R_(1)=1m, R_(2)=2m and masses M_(1) and M_(2) , respectively. The gravitational field due to sphere 1 and 2 are shown. The value of (M_(1))/(M_2)) is:

If M is a 3 xx 3 matrix, where det M=1 and MM^T=1, where I is an identity matrix, prove theat det (M-I)=0.

Let for A=[(1,0,0),(2,1,0),(3,2,1)] , there be three row matrices R_(1), R_(2) and R_(3) , satifying the relations, R_(1)A=[(1,0,0)], R_(2)A=[(2,3,0)] and R_(3)A=[(2,3,1)] . If B is square matrix of order 3 with rows R_(1), R_(2) and R_(3) in order, then The value of det. (2A^(100) B^(3)-A^(99) B^(4)) is

If M is the matrix [(1,-3),(-1,1)] then find matrix sum_(r=0)^(oo) ((-1)/3)^(r) M^(r+1)