Question

If A = `[("i", 2"i"),(-3, 2)] and "B" = [(2"i", "i"),(2, -3)]`, where `sqrt(-1)` = i,, find A + B and A – B. Show that A + B is a singular. Is A – B a singular ? Justify your answer.

Answer 1

A + B = `[("i", 2"i"),(-3, 2)] + [(2"i", "i"),(2, -3)]`

= `[("i" + 2"i", 2"i" + "i"),(-3 + 2, 2 - 3)]`

= `[(3"i", 3"i"),(-1, -1)]`

A – B = `[("i", 2"i"),(-3, 2)] - [(2"i", "i"),(2 , -3)]`

= `[("i" - 2"i", 2"i" - "i"),(-3 - 2, 2 - (-3))]`

= `[(-"i", "i"),(-5, 5)]`

Now, |A + B| = `|(3"i", 3"i"),(-1, -1)|`

= –3i – (– 3i) = 0

∴ A + B is a singular matrix.

Also, |A – B| = `|(-"i", "i"),(-5, 5)|`

= –5i – (– 5i) = 0

∴ A – B is also a singular matrix.