Only matrix A and matrix B have the same number of rows and columns. A and B can be added.

Question

Options

• ATrue
• BFalse

• A
  82% (23)
• B
  18% (5)

Explanation

Option A is correct because matrix addition requires that both matrices have identical dimensions - the same number of rows and the same number of columns - which the question confirms is true for A and B. When this condition is met, addition is performed element-by-element: each entry $a_{ij}$ is added to the corresponding entry $b_{ij}$, producing a result matrix of the same size. Option B is wrong because there is no additional constraint beyond matching dimensions; factors like the values inside the matrices or their names are irrelevant to whether addition is defined. A helpful memory tip: think of it as "same shape, can add" - if you can perfectly overlay one matrix on top of the other, their entries pair up and addition works.

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