`"If A"= ({:(2, 3),(5, 1):}), B = ({:(a, b),(c, d):})` and AB = -13I, then find the value of a + b - c + d.
(a) 5 (b) 3 (c) 2 (d) 1

Explanation

AB = -13I
`({:(2, 3),(5, 1):})({:(a, b),(c, d):}) = -13 ({:(1, 0),(0, 1):})`
`({:(2a+ 3c, 2b+3d),(5a+c, 5b+d):}) = ({:(-13, 0),(0, -13):})`
`rArr 2a + 3c =- 13 " "(1)`
`5a +c = 0 " " (2)`
`2a + 3d = 0 " " (3)`
`5b +d = -13 " " (4)`
Solving Eqs. (1) and (2), we get a = 1 and c=-5. Solving Eqs. (3) and (4), we get b = -3 and d=2.
a + b - c + d = 1 - 3 + 5 + 2 = 5.