1.

If `A = [[(2, 0)], [(5, -3)]] , B = [(-2, 1), (3, -1)] ` then find the trace of `(AB^T)^T`A. 10B. 14C. `-4`D. `-18`

Answer» Correct Answer - B
`A = ({:(2, 0), (5, -3):}) B =({:(-2, 1), (3, -1):})`
`B^(T) = ({:(-2, 3), (1, -1):})`
`A xx B^(T) = ({:(2, 0), (5, -3):}) ({:(-2, 3), (1, -1):})`
` = ({:(-4+10, 6-0), (-10-3, 15+3):}) = ({:(-4, 6), (-13, 18):})`
`(AB^(T))^(T) = ({:(-4, -13), (6, 18):})`
Trace of `(AB^(T))^(T) = -4 + 18 =14.`


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