If `[(2,-1),(1,0),(-3,4)]A=[(-1,-8,-10),(1,-2,-5),(9,22,15)]` , then sum of all the elements of matrix `A` is

Options

A. 0
B. 1
C. 2
D. `-3`

Answer

B

Explanation

Since the product matrix is `3xx3` matrix and the pre-multiplier of a is a `3xx2` matrix, therefore A is `2xx3` matrix. Let
`A=[(l,m,n),(x,y,z)]`. Then the given equation becomes
`[(2,-1),(1,0),(-3,4)][(l,m,n),(x,y,z)]=[(-1,-8,-10),(1,-2,-5),(9,22,15)]`
or `[(2l-x,2m-y,2n-z),(l,m,x),(-3l+4x,-3m+4y,-3n+4z)]=[(-1,-8,-10),(1,-2,-5),(9,22,15)]`
or `2l-x=-1, 2m-y=-8, 2n -z=-10`,
`l=1, m=-2, n=-5`
`implies x=3, y=4, z=0, l=1, m=-2, n=-5`
`implies A=[(l,m,n),(x,y,z)]=[(1,-2,-5),(3,4,0)]`