Find the matrix A such that

Given,

As A is multiplied with a matrix of order 3×2 and gives a resultant matrix of order 3×3

For matrix multiplication to be possible A must have 2 rows and as resultant matrix is of 3^rd order A must have 3 columns

∴ A is matrix of order 2×3

Let A = where a, b, c, d, e and f are unknown variables.

∴

∴ By matrix multiplication we have-

By equating the elements of 2 equal matrices we get-

a = 1 ; b = -2 and c = -5

also,

2a – d = -1 ⇒ d = 2a + 1 = 2 + 1 = 3

∴ d = 3

2b – e = -8 ⇒ e = 2b + 8 = -4 + 8 = 4

∴ e = 4

Similarly, f = 2c + 10 = 0

∴ A =