Find a nonzero row matrix B such that `B[(3,1),(-3,4)]=[(1,1)]`

Given A=[(1,3),(4,-3)] , find a nonzero column matrix B such that AB=3B .

Find a matrix B such that B[(a,0,0),(0,a,0),(0,0,a)]=[(1,0,0),(0,1,0),(0,0,1)], a ne 0

Find A+B if the matrices A and B are such that 2A+B=[(4,5),(3,8)], A+2B=[(2,4),(3,1)]

Find the inverse of the matrix A, if A=[(3,-2,3),(2,1,-1),(4,-3,2)]

Find the matrices A and B if 2A-B=[(3,-3,0),(3,3,2)], 2B+A=[(4,1,5),(-1,4,-4)]

Find the matrices A and B if A+2B=[(1,2,0),(6,-3,3),(-5,3,1)] and 2A-B=[(2,-1,5),(2,-1,6),(0,1,2)]

If A=[(1,2),(3,4)] , find a matrix B such that AB=I .

Examine the existence of inverse matrix and find the inverse matrix I it exists : A=[(1,2),(3,4)]

Express the matrix A as the sum of a symmetric matrix and a skew-symmetric matrix, where A=[(2,4,-6),(7,3,5),(1,-2,4)]