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ICSE Class 10 Mathematics Question 17 of 49

Multiple-Choice Questions — Question 17

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Question 17

If A = [ab] and [cd]\begin{bmatrix*}[r] a & b \end{bmatrix*} \text{ and } \begin{bmatrix*}[r] c \\ d \end{bmatrix*}, then :

  1. only matrix AB is possible

  2. only matrix BA is possible

  3. both matrices AB and BA are possible

  4. both matrices AB and BA are possible, AB = BA

Answer

Order of matrix A = 1 × 2

Order of matrix B = 2 × 1

Since, no. of columns in A is equal to the no. of rows in B and no. of columns in B is equal to the no. of rows in A.

∴ AB and BA are possible.

AB=[a×c+b×d]=[ac+bd].BA=[c×ac×bd×ad×b]=[cacbdadb].AB = \begin{bmatrix*}[r] a \times c + b \times d \end{bmatrix*} \\[1em] = \begin{bmatrix*}[r] ac + bd \end{bmatrix*}. \\[1em] BA = \begin{bmatrix*}[r] c \times a & c \times b \\ d \times a & d \times b \end{bmatrix*} \\[1em] = \begin{bmatrix*}[r] ca & cb \\ da & db \end{bmatrix*}.

∴ AB ≠ BA.

Hence, Option 3 is the correct option.