Multiple choice question — task. Mathematics State Board, Class 10.

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1. Which of the following can be calculated from the given matrices?

\(A =\)

(\begin{array}{l} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{array})

, \(B =\)

(\begin{array}{l} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array})

(i) \(A^2\)

(ii) \(B^2\)

(iii) \(AB\)

(iv) \(BA\)

(i) and (ii) only
(ii) and (iii) only
(ii) and (iv) only
all of these

2. If \(A =\)

(\begin{array}{l} 1 & 2 & 3 \\ 3 & 2 & 1 \end{array})

, \(B =\)

(\begin{array}{l} 1 & 0 \\ 2 & - 1 \\ 0 & 2 \end{array})

and \(C =\)

(\begin{array}{l} 0 & 1 \\ - 2 & 5 \end{array})

. Which of the following statements is correct?

(i)

AB + C = (\begin{array}{l} 5 & 5 \\ 5 & 5 \end{array})

(ii)

BC = (\begin{array}{l} 0 & 1 \\ 2 & - 3 \\ - 4 & 10 \end{array})

(iii)

BA + C = (\begin{array}{l} 2 & 5 \\ 3 & 0 \end{array})

(iv)

(AB) C = (\begin{array}{l} - 8 & 20 \\ - 8 & 13 \end{array})

(i) and (ii) only
(ii) and (iii) only
(iii) and (iv) only
all of these

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