Algebra

[2 0; 0 3], [5 0 0; 0 -1 0; 0 0 2]

A diagonal matrix has all non-diagonal elements as zero. Options 1 and 3 satisfy this condition as all elements except those on the main diagonal are zero.

[7 10; 15 22]

A² = A × A. Using matrix multiplication: [1 2; 3 4] × [1 2; 3 4] = [1×1+2×3 1×2+2×4; 3×1+4×3 3×2+4×4] = [7 10; 15 22].

[1 2; 3 4; 5 6]

The transpose of a matrix is obtained by interchanging rows and columns. B^T converts the 2×3 matrix to a 3×2 matrix where row 1 becomes column 1, etc.

Identity matrix

An identity matrix has 1s on the main diagonal and 0s elsewhere. This 3×3 matrix has exactly this pattern, making it the identity matrix I₃.