If A = {bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 {bmatrix} and B = {bmatrix} 1 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -3 {bmatrix}, then A² + B²= . . . . . . .

Correct Answer is : [50001300025]{bmatrix} 5 & 0 & 0 \\ 0 & 13 & 0 \\ 0 & 0 & 25 {bmatrix}50001300025

{bmatrix} 5 & 0 & 0 \\ 0 & 13 & 0 \\ 0 & 0 & 25 {bmatrix}

{bmatrix} 5 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 7 {bmatrix}

{bmatrix} 3 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 {bmatrix}

{bmatrix} 3 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 7 {bmatrix}

Correct Answer is : [50001300025]{bmatrix} 5 & 0 & 0 \\ 0 & 13 & 0 \\ 0 & 0 & 25 {bmatrix}50001300025

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GUJCET 2026 Math Paper

Question : 22 of 40

Marks: +1, -0

A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix}

B = \begin{bmatrix} 1 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -3 \end{bmatrix}

A^2 + B^2=

. . . . . . .

Solution:

Concept:

For a diagonal matrix, square each diagonal element separately.

Explanation:

Given

A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix}

A^2 = \begin{bmatrix} 2^2 & 0 & 0 \\ 0 & 3^2 & 0 \\ 0 & 0 & 4^2 \end{bmatrix} = \begin{bmatrix} 4 & 0 & 0 \\ 0 & 9 & 0 \\ 0 & 0 & 16 \end{bmatrix}

Given

B = \begin{bmatrix} 1 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -3 \end{bmatrix}

B^2 = \begin{bmatrix} 1^2 & 0 & 0 \\ 0 & (-2)^2 & 0 \\ 0 & 0 & (-3)^2 \end{bmatrix} = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 9 \end{bmatrix}

Now add corresponding diagonal entries:

A^2 + B^2 = \begin{bmatrix} 4+1 & 0 & 0 \\ 0 & 9+4 & 0 \\ 0 & 0 & 16+9 \end{bmatrix} = \begin{bmatrix} 5 & 0 & 0 \\ 0 & 13 & 0 \\ 0 & 0 & 25 \end{bmatrix}

Answer:

A^2 + B^2 = \begin{bmatrix} 5 & 0 & 0 \\ 0 & 13 & 0 \\ 0 & 0 & 25 \end{bmatrix}

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