If A -214415 and B -3-12 21 3- Write the orders of A B and B A-

The order of matrix A is 2 #215;3 and the order of matrix B is 3 #215;2. Since the number of columns in A is equal to the number of rows in B, AB exists a ...

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Standard XII

Mathematics

Triangular Matrix

If A =214415 ...

Question

If $A = [\begin{matrix} 2 & 1 & 4 \\ 4 & 1 & 5 \end{matrix}] and B = [\begin{matrix} 3 & - 1 \\ 2 & 2 \\ 1 & 3 \end{matrix}]$ . Write the orders of AB and BA.

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Solution

The order of matrix A is $2 \times 3$ and the order of matrix B is $3 \times 2$ .

Since the number of columns in A is equal to the number of rows in B, AB exists and it is of order $2 \times 2$ .
Also, since the number of columns in B is equal to the number of rows in A, BA exists and it is of order $3 \times 3$ .

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If A=214415and B=3-12 21 3. Write the orders of AB and BA.

The order of matrix A is 2×3 and the order of matrix B is 3×2. Since the number of columns in A is equal to the number of rows in B, AB exists and it is of order 2×2. Also, since the number of columns in B is equal to the number of rows in A, BA exists and it is of order 3×3.

If $A = [\begin{matrix} 2 & 1 & 4 \\ 4 & 1 & 5 \end{matrix}] and B = [\begin{matrix} 3 & - 1 \\ 2 & 2 \\ 1 & 3 \end{matrix}]$ . Write the orders of AB and BA.