Find matrix A such that ⎡⎢⎣2 -1 1 0 3⎤⎥⎦ A = ⎡⎢⎣ 5 1 9 6 2 2⎤⎥⎦

Given :⎡⎢⎣2 -1 1 0 3⎤⎥⎦ A = ⎡⎢⎣ 5 1 9 6 2 2⎤⎥⎦
A should have 2 rows, since it is multiplied with 3x2 and 2 columns as it gives the result as 3x2 matrix.
Let A = ⟨abcd⟩ ⟹ ⎡⎢⎣2 -1 1 0 3⎤⎥⎦ ⟨abcd⟩ = ⎡⎢⎣ 5 1 9 6 2 2⎤⎥⎦
⟹ ⎡⎢⎣2a - c 2b - d a + 0b + 0 0a + 4c 0b + 4d⎤⎥⎦ = ⎡⎢⎣ 5 1 9 6 2 2⎤⎥⎦
⟹ 2a - c = 5 (i)
2b - d = 1 (ii)
a + 0 = 1, b + 0 = 6 ⟹ a = 1 and b = 6
Substitute a in (i) we get 2(1) - c = 5 ⟹ c = 3
Substitute b in (ii) we get 2(6) - d = 1 ⟹ d = 4
Now, substitute the values of a, b, c and d in A we get A = ⟨1 6 3 4⟩