Matrix Calculator
Perform matrix operations — addition, subtraction, multiplication, determinant, transpose, and inverse. Supports 2×2 and 3×3 matrices. Essential for CBSE Class 12 and JEE Maths.
Matrix Calculator
Matrix A
Matrix B
Result
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Addition/Subtraction: Add or subtract corresponding elements. Both matrices must be the same size.
Multiplication: C[i][j] = sum of A[i][k] × B[k][j] for all k.
Determinant (2×2): det = ad − bc for matrix [[a,b],[c,d]].
Transpose: Rows become columns. Aᵀ[i][j] = A[j][i].
Inverse: A⁻¹ = adj(A) / det(A). Exists only if det ≠ 0.
Frequently Asked Questions
How do you multiply two matrices?
To multiply matrices A (m×n) and B (n×p), each element C[i][j] of the result is the dot product of row i of A and column j of B. The number of columns of A must equal the number of rows of B. This calculator handles square matrices (2×2 and 3×3).
What is the determinant of a matrix?
The determinant is a scalar value computed from a square matrix. For a 2×2 matrix [[a,b],[c,d]], det = ad − bc. For a 3×3 matrix, it is computed by cofactor expansion. A matrix is invertible if and only if its determinant is non-zero.
How do you find the inverse of a matrix?
For a 2×2 matrix: swap diagonal elements, negate off-diagonal elements, and divide by the determinant. For a 3×3 matrix: find the cofactor matrix, transpose it to get the adjugate, then divide by the determinant. The matrix must have a non-zero determinant.
Where are matrices used in JEE and CBSE?
Matrices are covered in CBSE Class 12 Chapter 3 (Matrices) and Chapter 4 (Determinants). In JEE, matrices appear in solving systems of linear equations (Cramer's rule), transformations, and eigenvalue problems. They carry significant weightage in board and entrance exams.