Inverse Of A Matrix

Question

For the two by two matrix A with rows (4, 7) and (2, 6), the inverse matrix A inverse, computed using the adjoint over determinant formula, has which top-left entry?

RankGuru · Accepted Answer

The inverse of a two by two matrix is the adjoint divided by the determinant, a standard JEE Advanced computation valid only when the determinant is non-zero. For A with rows (4,7),(2,6), the determinant is 4·6 - 7·2 = 24 - 14 = 10, which is non-zero so the inverse exists. The adjoint swaps the diagonal entries and negates the off-diagonal entries, giving adj(A) with rows (6, -7),(-2, 4). Dividing by the determinant 10, the inverse has rows (6/10, -7/10),(-2/10, 4/10). The top-left entry is 6/10 = 3/5 in simplest form. Option 2/5 wrongly takes the bottom-right entry 4/10 without swapping diagonals. Option -7/10 is the top-right off-diagonal entry, not the top-left. Option 1/4 ignores the determinant scaling and merely reciprocates the (1,1) entry of A. Hence the top-left entry is 3/5. Plausibility check: multiplying A by the proposed inverse should yield the identity, and the (1,1) entry 4·(6/10) + 7·(-2/10) = (24 - 14)/10 = 1 confirms the inverse is correct.

Inverse Of A Matrix

Select the correct option:

🔒 Solution Hidden from View

More matrices and determinants Practice Questions

The area of the triangle with vertices at the points (1, 2), (4, 6) and (7, 2) in the coordinate pla...

Let A be the two by two matrix with rows (2, 1) and (1, 2); using the Cayley-Hamilton theorem, the m...

For any skew-symmetric matrix of odd order, the determinant always takes a fixed value; the determin...

The homogeneous system of equations with coefficient matrix rows (1, 2, 3), (2, k, 6) and (1, 1, 1) ...

The value of the real parameter k for which the matrix with rows (k, 2, 3), (2, k, 1) and (3, 1, k) ...

If A and B are square matrices of order 3 with det(A) = 3 and det(B) = -2, then the determinant of t...

A square matrix A is called idempotent when it satisfies A squared equal to A; for such a matrix the...

If A is a square matrix of order 2 with trace equal to 5 and determinant equal to 6, then the sum of...

A square matrix A is nilpotent if some positive integer power of A equals the zero matrix; the deter...

Applying the property that adding a multiple of one row to another leaves a determinant unchanged, t...

For two invertible square matrices A and B of the same order, the inverse of the product AB is corre...

A real square matrix A is orthogonal when it satisfies the relation A transpose times A equal to the...

About This Question

Solution