Question

If A = 1 -2 3 4 , B = 5 3 4 1 and C = 0 7 -3 8 then Prove,
Commutative Law Under Addition
Associative law Under Multiplication
Distributive Law of multiplication over subtraction
(AB)-1 = B-1A-1
(BC)t= BtCt​

Answer 1

Given,

A = 1 -2 3 4

B = 5 3 4 1

C = 0 7 -3 8

To prove,

Commutative Law Under Addition

Associative law Under Multiplication

Distributive Law of multiplication over subtraction

Solution,

(A+B) +C = A+ (B+C)

(1+5)+0 = 1+(5+0)

6+0= 1+5

6=6

L.H.S=R.H.S

Hence, commutative law under addition will be (AB)-1 = B-1A-1, (BC)t= BtCt.