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Question
If A = `[(1, 2, 3),(3, 2, 1)]`, B = `[(1, 0),(2, -1),(0, 2)]` and C = `[(0, 1),(-2, 5)]` Which of the following statements are correct?
(i) AB + C = `[(5, 5),(5, 5)]`
(ii) BC = `[(0, 1),(2, -3),(-4, 10)]`
(iii) BA + C = `[(2, 5),(3, 0)]`
(iv) (AB)C = `[(-8, 20),(-8, 13)]`
Options
(i) and (ii) only
(ii) and (iii) only
(iii) and (iv) only
all of these
Solution
(i) and (ii) only
Explanation;
Hint:
(i) AB + C : order of A = 2 × 3
order of B = 3 × 2
order of AB = 2 × 2
order of C = 2 × 2
It is possible to add AB + C
(ii) BC :
order of B = 3 × 2
order of C = 2 × 2
It is possible to find BC
(iii) BA is not possible
order of B = 3 × 2
order of A = 3 × 2
BA does not exist.
BA + C is not a correct statement
(iv) ABC is not possible
order of A = 2 × 3 order of
B = 3 × 2
order of AB = 2 × 2
order of C = 3 × 2
It is not possible to multiply AB and C.
∴ The statement ABC is not correct.
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