Find the matrices A and B when `A+B = 2B^(t) and 3A+2B=I_(3)` where `B^(t)` denotes the transpose of B and `I_(3)` is the identity matrix of order 3.

If the matrix A=1/3 {:((a,2,2),(2,1,b),(2,c,1)):} obeys the law "AA"'=I, find a,b,and c (Here A' is the transpose of A and I is the unit matrix of order 3).

If A and B are square matrices of order 3 such that A^(3)=8 B^(3)=8I and det. (AB-A-2B+2I) ne 0 , then identify the correct statement(s), where I is identity matrix of order 3. (A) A^(2)+2A+4I=O (B) A^(2)+2A+4I neO (C) B^(2)+B+I=O (D) B^(2)+B+I ne O

Let A and B be two square matrices of order 3 and AB=O_3 , wher O_3 denotes the null matrix of order 3. Then,

If A={:((3,2),(3,3))and B={:((1,-2/3),(-1,1)) show that AB=I_(2) where I_(2) is the unit matrix of order 2.

Given the matrices A and B as A=[(1,-1),(4,-1)] and B=[(1,-1),(2,-2)] . The two matrices X and Y are such that XA=B and AY=B , then find the matrix 3(X+Y)

Find the matrices A and B for which: A-2B={:((-7,7),(4,-8)) and A-3B={:((-11,9),(4,-13))

Match the statement/expressions in Column I with the statements/expressions in Column II. Column I Column II The minimum value of (x^2+2x+4)/(x+2) is (p) 0 Let Aa n dBb e3x3 matrices of real numbers, where A is symmetric, B is skew symmetric, and (A+B)(A-B)=(A-B)(A+B) if (A B)^t=(-1)^kA B , where (A B)^t is the transpose of the matrix A B , then the possible values of k are (q) 1 Let a=(log)_3(log)_3 2. An integer k satisfying 1<2^(-k+3^((-1)))<2, must be less than (r) 2 In sintheta=cosvarphi, then the possible values of 1/pi(theta+-varphi-pi/2) are (s) 3

A and B arer two matrices of order 3 × 3 which satisfy AB = A and BA = B. then (A+I)^(5) is equal to (where I is identify matrix)___

Let A and B be 3xx3 matrtices of real numbers, where A is symmetric, "B" is skew-symmetric , and (A+B)(A-B)=(A-B)(A+B)dot If (A B)^t=(-1)^k A B , where . (A B)^t is the transpose of the mattix A B , then find the possible values of kdot

Let A and B be two non-singular matrices such that A ne I, B^(3) = I and AB = BA^(2) , where I is the identity matrix, the least value of k such that A^(k) = I is