We have\(\begin{bmatrix} 2 & -1\\ 1 & 0\\ -3 & 4\end{bmatrix}\). A = \(\begin{bmatrix} -1 & -8 & -10\\ 1 & -2 & -5\\ 9 & 22& 15\end{bmatrix}\)

This matrix multiplication is possible only when the order of matrix is 2 × 3. Let matrix A = \(\begin{bmatrix} a & b & c\\ d & e & f\\ \end{bmatrix}\).

Therefore, \(\begin{bmatrix} 2 & -1\\ 1 & 0\\ -3 & 4\end{bmatrix}\)\(\begin{bmatrix} a & b & c\\ d & e & f\\ \end{bmatrix}\) = \(\begin{bmatrix} -1 & -8 & -10\\ 1 & -2 & -5\\ 9 & 22& 15\end{bmatrix}\)

By equality of two matrices, comparing corresponding components, we get 

a = 1, b = −2, c = −5. (By comparing corresponding components of 2^nd row of both matrices. ) 

2a − d = −1, 2b − e = −8, 2c − f = −10. 

d = 2a + 1 = 2 + 1 = 3, e = 2 + 8 = −4 + 8 = 4, f = 2 + 10 = −10 + 10 = 0. 

(By comparing corresponding components of 1^st row of both matrices and putting values of a, b and c. ) We clearly see that values of a,b,c,d,e and f satisfies by corresponding components of 3^rd row of both matrices. 

Therefore, matrix = \(\begin{bmatrix} a & b & c\\ d & e & f\\ \end{bmatrix}\) = \(\begin{bmatrix} 1 & -2 & -5\\ 3 & 4 & 0\\ \end{bmatrix}\)