Question

Prove that a + X equals to zero has a unique solution for all Matrix m into n. ( m×n)

Answer 1

Suppose Y is another solution

Suppose Y is another solutionWe have A+X =0

Suppose Y is another solutionWe have A+X =0and also A+Y=0

Suppose Y is another solutionWe have A+X =0and also A+Y=0Subtracting gives X-Y = 0 and so X = Y making X the unique solutioon