CUET UG 2025 — Mathematics Arithmetic

Matrix B is 3×2 and matrix A is 2×3.

The number of columns in B equals the number of rows in A, so BA can be computed.

The result BA will be a 3×3 matrix.

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$$BA = \begin{bmatrix} 2 & -3 \\ 4 & -5 \\ 2 & -1 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 \\ -4 & -5 & -2 \end{bmatrix}$$BA=​242​−3−5−1​​[1−4​2−5​3−2​]

Row 1 of B with each column of A:

$$(1,1): 2(1) + (-3)(-4) = 2 + 12 = 14$$(1,1):2(1)+(−3)(−4)=2+12=14

$$(1,2): 2(2) + (-3)(-5) = 4 + 15 = 19$$(1,2):2(2)+(−3)(−5)=4+15=19

$$(1,3): 2(3) + (-3)(-2) = 6 + 6 = 12$$(1,3):2(3)+(−3)(−2)=6+6=12

Row 2 of B with each column of A:

$$(2,1): 4(1) + (-5)(-4) = 4 + 20 = 24$$(2,1):4(1)+(−5)(−4)=4+20=24

$$(2,2): 4(2) + (-5)(-5) = 8 + 25 = 33$$(2,2):4(2)+(−5)(−5)=8+25=33

$$(2,3): 4(3) + (-5)(-2) = 12 + 10 = 22$$(2,3):4(3)+(−5)(−2)=12+10=22

Row 3 of B with each column of A:

$$(3,1): 2(1) + (-1)(-4) = 2 + 4 = 6$$(3,1):2(1)+(−1)(−4)=2+4=6

$$(3,2): 2(2) + (-1)(-5) = 4 + 5 = 9$$(3,2):2(2)+(−1)(−5)=4+5=9

$$(3,3): 2(3) + (-1)(-2) = 6 + 2 = 8$$(3,3):2(3)+(−1)(−2)=6+2=8

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$$BA = \begin{bmatrix} 14 & 19 & 12 \\ 24 & 33 & 22 \\ 6 & 9 & 8 \end{bmatrix}$$BA=​14246​19339​12228​​

From the resulting matrix:

$b_{23} = 22$b23​=22 (row 2, column 3)

$b_{31} = 6$b31​=6 (row 3, column 1)

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$$b_{23} - b_{31} = 22 - 6 = 16$$b23​−b31​=22−6=16

Therefore, $(b_{23} - b_{31}) = 16$(b23​−b31​)=16